(among other things, because they were suspicious that those so chosen would renege rather than carry out the mission)
Let’s say somebody who flies out with extra bombs instead of fuel has an overall 0.1% chance of making it back alive through some heroic exploit. Under the existing system, with 25% survival, you’re asking every pilot to face two half-lives worth of danger per mission. With extra bombs, that’s half as many missions, but each mission involves ten half-lives worth of danger. Is it really all that rational to put the pilots in general in five times as much danger for the same results? After all, drawing the long straw doesn’t mean you’re off the hook. Everybody’s going to have to fly a mission sooner or later.
Thinking in terms of “half-lives of danger” is your problem here; you’re looking at the reciprocal of the relevant quantity, and you shouldn’t try and treat those linearly. Instead, try and maximize your probability of survival.
It’s the same trap that people fall into with the question “if you want to average 40 mph on a trip, and you averaged 20 mph for the first half of the route, how fast do you have to go on the second half of the route?”
“if you want to average 40 mph on a trip, and you averaged 20 mph for the first half of the route, how fast do you have to go on the second half of the route?”
How do you answer this question?
Edit: MBlume kindly explained offsite before the offspring comments were posted. Er, sorry to have wasted more people’s time than I needed.
It’s still an interesting exercise to try to come up with the most intuitive explanation. One way to do it is to start by specifying a distance. Making the problem more concrete can sometimes get you away from the eye-glazing algebra, though of course then you need to go back and check that your solution generalizes.
A good distance to assign is 40 miles for the whole trip. You’ve gone 20 mph for the first half of the trip, which means that you traveled for an hour and traveled 20 miles. In order for your average speed to be 40 mph you need to travel the whole 40 miles in one hour. But you’ve already traveled for an hour! So—it’s too late! You’ve already failed.
Yes, that’s roughly how MBlume explained it (edited for concision and punctuation):
MBlume: I can help you! or could if there was an answer...
Alicorn: Good, I can delete the comment before it gets downvoted again! I half-suspected there was not, and that it depended on the distance of the journey, but wasn’t sure
MBlume: that is a silly thing for people to downvote. it doesn’t actually, but it is impossible. you have to cover the rest of the distance instantly to average 40mph
Alicorn: Oh, and they won’t let your car onto the transporter pad, gotcha
MBlume: nodnod
Alicorn: …why do you have to cover the distance instantly?
MBlume: (they are jerks.) because… let’s pretend the distance is 40 miles. in order to average 40 mph
Alicorn: you need to get there in an hour
MBlume: you would have to cover the whole distance in an hour, nodnod
Alicorn: ahhhh, now I see.
MBlume: but you drive half of that (20 miles) at 20 mph… nodnod
Alicorn: you took an hour to go 20 miles at—yes. that.
It felt like I was following, say for analogy, a discussion among filipinos who were switching back and forth between English and Tagalog. But re-reading it twice I started to get the flow and terms. E.g. “nodnod” was opaque initially.
There was me, that is Alex, and my three droogs, that is Pete, Georgie, and Dim, and we sat in the Korova Milkbar trying to make up our rassoodocks what to do with the evening. The Korova milkbar sold milk-plus, milk plus vellocet or synthemesc or drencrom, which is what we were drinking. This would sharpen you up and make you ready for a bit of the old ultra-violence.
Yes, that movie is a nice example of science fiction which deliberately makes up new words (so I presume) to give the viewer that fish out of water “it’s the future” feeling. Star Trek does something like that which I think is called technobabble, which is also deliberately incomprehensible with a sciency twist. I get much the same feeling when I watch certain popular shows from English- but not American-speaking places, where people combine unknown references, unknown words, and pronunciation which I have to struggle to unravel.
Happily, in all cases the simple act of patiently familiarizing myself by repeated viewing works well to bring me up to speed, though I personally have never gone as far as learning Klingon.
Yes, that movie is a nice example of science fiction which deliberately makes up new words (so I presume) to give the viewer that fish out of water “it’s the future” feeling.
If I remember correctly, it’s a blend of English, Russian, and Latin.
I guess it is rather bizarre. But most of the unusual conventions on IRC and other chat services are in order to make it more like a face to face conversation. They generally either allow you to narrate yourself from a third person perspective, or speed up common interactions that take much longer to type than they do in real life.
Although “nodnod” seems unusually nonsensical, since it takes longer to type than “yes”. I cannot say I have seen that used before.
I don’t doubt it. That’s why I said that I felt that I was getting old for the world. The unusual, out of place thing is me. I’m assuming that the chat log is typical.
d = (average speed) (time)
time = d / (average speed)
So if your average speed is 40 (mph), your total time is d/40.
You have already travelled half the distance at speed 20 (mph), so that took time (d/2)/20 = d/40. Your time left to complete the trip is your total time minus the time spent so far: d/40 - d/40 = 0. In this time you have to travel the remaining distance d/2, so you have travel at a speed (d/2)/0 = infinity, which means it is impossible to actually do.
Let t1 be the time taken to drive the first half of the route.
Let t2 be the time taken to drive the second half.
Let d1 be the distance traveled in the first half.
Let d2 be the distance traveled in the second half.
Let x be what we want to know (namely, the average speed during the second half of the route).
Then the following relations hold:
40 (t1 + t2) = d1 d2.
20 * t1 = d1.
x * t2 = d2.
d1 = d2.
Use algebra to solve for x.
To average 40 mph requires completing the trip in a certain amount of time, and even without doing any algebra, I notice that you will have used all of the available time just completing the first half of the trip, so you’re speed would have to be infinitely fast during the second half.
I am pretty confident in that conclusion, but a little algebra will increase my confidence, so let us calculate as follows: the time you have to do the trip = t1 + t2 = d1 / 40 + d2 / 40, which (since d1 = d2) equals d1 / 20, but (by equation 2) d1 / 20 equals t1, so t2 must be zero.
I expect a high probability of this explanation being completely useless to someone who professes being bad at math. Their eyes are likely to glaze over before the half way point and the second half isn’t infinitely accessible either.
I already had the problem explained to me before I saw the grandparent, but I think you’re right—I might have been able to puzzle it out, but it’d have been work.
I first started long-distance running when I was 20 years old. Up until that moment I hated everything about running, especially the sharp pain in my lungs whenever I ran more than 50 meters or so. But as soon as I gave it a serious try, the pain went away completely after about a week of morning runs, and from that day it never came back. Now I love running. And sometime later I found out that long-distance running is one of the few areas where humans can beat pretty much every animal out there. Something we’re naturally good at.
Another such area is intelligence.
I know that you are an intelligent person, whatever your other flaws. And I don’t completely understand what can stop an intelligent person from solving trivial puzzles such as orthonormal’s original question. Could your perception of “it’d be work” be the mental equivalent of lung pain that unexperienced runners have? Something that would just go away forever if you gave it a week of effort?
Well, in the department of actual running, I have some kind of mysterious lung issue that means I need to gasp for air a lot even when I’m sitting still and have been for hours and it only gets worse if I try to do exercise more strenuous than a leisurely walk. (Armchair diagnoses appreciated, incidentally—so far I’ve stumped multiple doctors and new Google keywords are good.)
Here is something like the thought process that goes through my head when I encounter a problem of this approximate type:
I know what all those words mean. I could come up with a toy scenario and see what’s interesting about this problem, that someone bothered to bring it up.
It might be the sort of question where coming up with one toy scenario doesn’t answer it because for some reason it doesn’t generalize. Like it could have to do with the distance. I don’t want to come up with five different distances and work it out for all of them. I’d probably make an arithmetic mistake anyway. I can barely compose a mathematically accurate D&D character, and I’m way more motivated there than here. I’m not interested enough in this to do it in a calculator and then re-read the ticker tape. My eyes are swimming just thinking about it.
And because I’m not good at this, I would be reasonably likely to get it wrong, and then, no matter how much time I’d put into it myself, I would need to ask someone. I could get help if I asked. I am cute and friendly and there are helpful people around. I could get help even if I didn’t work on it myself. That would be faster, and then I’d know the answer, and I have to ask anyway, so why not just ask? Why not save the work, and not risk wasting a lot of time on getting a wrong answer and having to stare at all those numbers?
Record yourself (audio and video) during one of your attacks and I’ll have a much better idea. Right now, it’s extremely hard to tell from your description. Obviously, actually listening to you with a stethoscope and being able to perform a few tests would help me even more, of course.
By “attack” do you mean “one of the hundreds of occasions throughout an average day where I attempt to take an especially deep breath to satisfy my customary air hunger” or do you mean “run around until you collapse, gasping, and record that”?
Ok, but those are all exercise. Do you ever get attacks from cold, from allergens, from waking up in the middle of the night, from fear, from pain, from eating too much before bedtime?
Cold weather can make getting my deep breaths uncomfortable, but doesn’t seem to make me need more of them. I’m not allergic to anything except mushrooms (and that causes nausea, not breathing problems). I’ve never woken up in the middle of the night (that I know of) with breathing problems. I sometimes breathe oddly when afraid/in pain, but it doesn’t seem related. Eating too much at bedtime doesn’t do anything that eating too much at other times doesn’t.
Sorry for deleting my comment. I’ve been doing this a lot lately—I write something and then notice that it’s stupid for one reason or another. (In this case it was the armchair diagnosing/other-optimizing.) Didn’t think you’d react so fast.
Well your last paragraph was interesting in a way. In fact I don’t understand it. The point of a puzzle is to stretch and work out your brain, not arrive at an answer asap. If you have a bus full of hostages whose fate depends on an arithmetical problem, it’s indeed wiser to ask someone else. But such situations don’t occur often. In fact I sometimes explicitly ask other people to avoid giving me any hints because I want to solve the puzzle myself. Asking for help is analogous to taking the bus instead of your morning run :-)
But well, I guess if you don’t enjoy puzzles already, then saying things like “c’mon jump in, the water’s fine” isn’t going to influence you much. Some things you really have to try before you can see the fun contained within. I think most things I enjoy in life fall in this category...
I hate being frustrated. It happens to me very easily. I hate not knowing the endings to stories, I hate not knowing what I’m getting for my birthday, and the only way I can not hate not knowing the answers to math problems is by not giving a flying fuck about them at all—which isn’t conducive to expending effort on solving them. I’ve generalized the “stop giving a fuck” self-defense strategy to other hatreds-of-not-knowing stuff, mostly to discourage people from teasing me with this neurosis. I believe that other people can enjoy various forms of not-knowing-stuff, or fail to hate it enough to override some competing desire to achieve knowledge on their own. But I don’t.
So basically, I looked at that math problem, sort of cared about knowing the answer, and asked. I got an answer (actually, several) which were quick enough to suit me. If the only way I could have learned the answer were to work it out for myself—or sit through ten minutes of algebra lessons or something—then I would have defensively ceased to care, instead.
Once I know the answer—in this case, that after having gone halfway at 20mph, you need to teleport to get to point B in time—then I can tolerate some further discussion of the scenario or the underlying math (although not arbitrary amounts). This is much the same as how, when I know that character X and character Y in some story eventually get together (or find the MacGuffin, or die, or whatever major plot item), I can often put up with extended periods of wondering exactly when and how.
I’ve found in the past that I remember the right answer better if I can guess it first and then get confirmation. It doesn’t help when I guess wrong, but when I guess right it’s a win.
The lung thing has gone on for several years; I have a memory that doesn’t make sense without it that has to have taken place in fall 2006. I don’t remember exactly when it started but I have not always had it. (I suspect it began sometime after I started taking iron to treat my anemia, since no one ever connected the two; that would’ve been some months after I turned 17, so, late 2005-early 2006).
It does vary day to day and hour to hour, plus with what I’m doing (walking excessively briskly, or jumping around, or otherwise being active, makes it act up—it was outright crippling on one occasion last summer when I tried to bike a few blocks; I had to pull over and sit on the sidewalk for a while and then verrrrry carefully bike back, walking the thing up hills and only riding on levels and downhill.) There is an overall trend of worsening from year to year.
I suspect it began sometime after I started taking iron to treat my anemia, since no one ever connected the two; …
Who is ‘no one’ and which two did they fail to connect? Why do you say ‘since’?
I’m not a doctor. But it sure sounds to me that your blood is just not carrying enough oxygen to support vigorous exercise. Which is by definition ‘anemia’. Which comes in various forms, the most common of which can be treated by iron supplements, but the most serious of which have other causes and treatments. Just from what I read on the web, my guess would be you have ‘pernicious anemia’.
I would strongly advise going to a doctor again, and asking for blood tests. Be sure the doctor is informed about any ways in which your diet is unusual. Good luck.
“No one” is a couple of internists, my dad and my uncle (both doctors), and various random people I mentioned it to. What I mean is that people who know I used to be anemic and that I now have this dyspnea problem have never asked “I wonder if you still have [anemia-related subcondition] and that’s causing the dyspnea?”
The iron pills working was confirmed with a blood test. Before I took iron pills, my readings on some relevant feature of my blood were so low that I ought to have been fainting on a regular basis; after they were in normal range and I’ve been allowed to give blood several times since.
Asthma/reactive airway disease seems like the obvious thing here, so has that been ruled out? Did they have you blow into a thing to measure whether you were breathing a normal volume of air (spirometry)?
I have never had to blow into a thing. Since I have consulted plural doctors about this, I’m not sure why none of them would have thought of athsma if that were consistent with my symptoms. Why might that be?
Asthma usually shows up in childhood, not at 17, and maybe some of the doctors you saw assumed that previous doctors would have checked out the possibility of asthma already. The definitive test for asthma is called a methacholine challenge; basically you inhale a chemical that irritates your lungs, and if you’re asthma-prone then you have trouble breathing (there is no physical activity involved).
It probably isn’t a heart issue if you haven’t always had it...those are usually congenital...but I could be wrong. (Also not a doctor). But it sounds very debilitating, and worth fixing.
I have never had to blow into a thing. Since I have consulted plural doctors about this, I’m not sure why none of them would have thought of athsma if that were consistent with my symptoms. Why might that be?
That is troubling. Even if it isn’t asthma it is definitely something to do with the lungs that influences breathing. Measurement of breathing capabilities should be one of the first things they do!
Honestly? No idea. Nursing student here, in no way a doctor. But if I were you I’d go to a doctor and describe my symptoms and say “Could I have asthma?” I’m thinking most likely outcome is they give you some meds to try, which could be a good thing, you know? Certainly before you go after any of the zebras you’ll get by Googling around.
My other thought is it could even be a heart issue, if your lungs check out. I’m kind of..surprised...that no one is more concerned about an apparently healthy young person being unable to breathe, so I’m guessing your oxygen saturation isn’t dropping to scary levels or anything.
Well, I’ve never passed out, and I tend not to take much exercise that this is interfering with, and doctors in general like to say that absolutely everything that could possibly be wrong with me will be fixed with exercise, which advice I ignore, which can then go on indefinitely “explaining” my problem. (I went in with little muscle twitches in my legs and eyelids once—I still get those, still don’t know what they are—doctor says, “Consider getting more exercise”. Exercise my eyelids, right? I’m not blinking enough?)
I went in with little muscle twitches in my legs and eyelids once—I still get those, still don’t know what they are—doctor says, “Consider getting more exercise”. Exercise my eyelids, right? I’m not blinking enough?
Clearly that is not what they are suggesting. Generalised exercise does clear up some such twitches. It may not in your case and it is even conceivable that you could die trying. But regardless the exercise suggestion in response to that complaint is not absurd or a valid target of mockery.
If this were the only thing doctors bizarrely said I should exercise for, I could shrug and say that maybe there is a mystical eyelid-exercise connection.
But I get told this a lot (mysterious lumps on your back? Exercise! Left foot makes a crunchy noise when you move it like so? Consider the benefits of exercise. You get lots of headaches? Try exercising! Sometimes the palms of your hands swell up for no reason? I recommend more exercise. You keep getting ingrown toenails? That may go away with enough exercise. If you exercise, you can’t breathe? Maybe you should fix that with exercise.)
I’m pretty sure that they’re coming up with this too quickly, for too many things, which means I’m suspicious of each instance of advice to get more exercise (for a specific problem; I’m tired of, but not suspicious of, the advice that it would just be a good idea in general.) I think it is more likely that they are saying this because I’m fat, not because it’s related to the problems I go in with. Often I am not even asked how much I exercise before a health professional says I need to do more of it.
I’m pretty sure that they’re coming up with this too quickly, for too many things, which means I’m suspicious of each instance of advice to get more exercise (for a specific problem; I’m tired of, but not suspicious of, the advice that it would just be a good idea in general.)
Perhaps more importantly it sounds like they come up with ‘exercise’ then stop. For many things exercise will help, even if only indirectly, but it certainly isn’t the primary treatment. Sure, exercise is great for asthma, but so are steroids—and sometimes the former isn’t enough. Likewise for blood pressure and heart disease. Come to think of it exercise is great for the symptoms of being a chronic smoker… but if the doctor stopped at ‘exercise more’ without going on to ‘stop smoking dumbass!’ there would be a problem!
I think it is more likely that they are saying this because I’m fat, not because it’s related to the problems I go in with.
Apart from being interpersonally rude that doesn’t seem to reflect well on their medical competence. There is a relationship between exercise and fat storage but it isn’t all that strong. Doctors aren’t supposed to be going along with popular stereotypes!
I’m reminded of the day I was running my first marathon. I was up to the 30km mark and starting to feel it. Then along beside me comes a guy built like a 44 gallon drum on legs. He was puffing away but looked like he was ready to run another 30km then maybe do it again after lunch. While I was slowing down with fatigue and complete glycogen depletion he was accelerating. That rather completely destroyed any preconceptions I may have had that people with a high bodyfat ratio must not exercise.
Often I am not even asked how much I exercise before a health professional says I need to do more of it.
It’s scary, but I have no problems believing that. Along similar lines my father’s doctor (well, former doctor) concluded from his high cholesterol on his bloodwork that he clearly eats too much fast food and needs to cut back on the KFC. Where was that doctor when the studies were published regarding just what the limits of the influence of diet on cholesterol are? Even worse is my mother’s (former) doctor insisting that she is a long term alcoholic and needs help, despite her protestation to the contrary. She hasn’t consumed a drop of alcohol in her entire life. The high indicators of liver strain are a known side effect of the rather potent medication she takes for neuropathic pain.
I often wonder just how some of these people go through a decade of training and still end up clueless.
I’ll track it down if you care, but I just read something which claims that twitching eyelids are a minor side effect of stress. This does seem to be true for me.
For some people, exercise lowers their stress level, so the doctor’s advice isn’t entirely crazy.
On the other hand, casual surveying has turned up a shockingly consistent result that only about 20% of doctors listen and think. This implies that you need to be persistent if you need a diagnosis for something that’s even a little weird.
Even fairly easy problems like celiac can take a surprisingly long time to get diagnosed.
Exercise raises my stress level. (One time, exactly one, in my entire life, I felt sort of high after getting some exercise. I thought it was cool and tried to reproduce it and couldn’t.) Even if I’m just walking, gently enough that my lungs don’t care, it makes my feet hurt and the rest of me too hot until all I want to do is fling myself into a frigid shower and collapse until I’m cold enough to believe that it’s safe to leave the water. (I routinely arrange to be too cold, because definitely being too cold is safer and more comfortable than maybe being too hot.)
Oh, you totally should get more exercise, and they are right to tell you that, although maybe they would have better luck if they came across as more helpful. But I’m a slug too and I can breathe ok; I just can’t run very far. I still vote asthma.
Is there any reason to think that more exercise will be good for her?
More exercise is generally good for most people, which is one reason. Aerobic exercise tends to increase aerobic capacity, and decreases the risk of plenty of chronic diseases.
Alicorn admits she doesn’t get much exercise, so she’s clearly not in the tail of people who already exercise strenuously enough that more exercise would be harmful. Light exercise like I suggested is very unlikely to do any harm, and could very well even help her symptoms by improving her endurance.
By way of clarification, I do not intend to blame Alicorn for her symptoms. I understand why she might feel that way, and I regret that she has been made to feel dismissed in the past. My suggestion that she see a doctor and ask about asthma is much more urgent and important, so I want to reemphasize it rather than get stuck on the question of exercise.
Alicorn has implied that she isn’t completely sedentary or bedridden—she goes out walking, and sometimes gets seriously out of breath. Is there any reason to think that more exercise will be good for her?
Not exercising is a problem for anybody regardless of whether they have a breathing problem or not. It raises your chances of obesity, which later on can lead to lots of nasty consequences, and I think sedentary people show an increase in certain chronic diseases (heart disease for sure, type 2 diabetes possibly but I don’t remember for sure) regardless of weight. In that sense, more exercise would be good for Alicorn.
That being said, I think it’s misleading to say it would directly fix her mystery respiratory problem. (Even if it turns out to be asthma...exercise doesn’t cure asthma and can even trigger it for certain people). It might improve the symptoms in the long run. It might not. There might be another way to improve the situation enough that she can exercise.
I’m half convinced. However, I keep reading that inactivity is unhealthy regardless of whether it is fattening. Therefore fat people have good reason to try to resist the tendency to inactivity induced in them by their fatness.
So: why are fat people inactive? My only tentative guess is that it is difficult for them to move their bodies, and they respond to the difficulty by moving less. This suggests the following possible remedy: strength training. With stronger muscles, your body feels like less of a burden, and so you are more likely to move around.
So: why are fat people inactive? My only tentative guess is that it is difficult for them to move their bodies, and they respond to the difficulty by moving less.
Very plausible. Also, fear and embarrassment could be factors. Several of my heavier friends have told me that they don’t like to go to the gym because they feel self-conscious surrounded by fitter people. This is probably also true of, for example, jogging in public; they are afraid of people watching them and judging them (“Look at that fat guy/girl trying to run!”).
Yes, this was the basis for a Jerry Seinfeld comedy routine: “We need to have a pre-gym, a gym-before-the-gym. A place where you can get yourself fit enough to be comfortable going to the regular gym.” (And this actually isn’t far from the reason for the success of the franchise Curves.)
I was strongly voted up a while back for making the above point and then suggesting we have the analog website for LessWrong—a place where people can learn and discuss this stuff without being intimindated by those who know more.
The study (which needs significant followup to create usable results) could have a number of interpretations, including:
*conclusions not fully supported by the data
*obesity leads to less enjoyment of motion
*obesity leads to fewer social opportunities to engage in sports
*low socio-economic status leads to obesity and to inactivity (due to insufficient access to parks, to parents who force you out of the house, etc).
*People don’t record their activity levels every day, so their estimates are colored more by measurable factors (body weight) than by unmeasurable ones (how much they actually moved).
Valid point. I’ve read that for sedentary people, starting an exercise regime is a poor way to lose weight. I still think it’s an excellent way not to gain weight in the first place...children who active, who remain active as teenagers and young adults (and don’t grossly overeat) probably won’t put on the weight in the first place. I did an energy-expenditure study that showed I burn nearly 3000 calories a day, mainly because I can maintain an ‘intense’ level of exercise for an hour or more, whereas someone who is unfit and overweight already probably can’t and so wouldn’t burn nearly as many calories. Muscle mass also burns more calories at rest than fat tissue, so that someone at a high level of fitness can eat more even on days when they don’t exercise.
The moral of the story: I’m going to put my kids in one physical activity after another (like my parents did with my siblings and myself) until they find one they can stick with, and I’m going to try to keep it a part of family life. After all, it takes far less willpower to maintain a lifelong habit than to start a new regime once you start putting on weight.
I was in exactly the same situation when I was 15 before I was diagnosed with asthma, probably worse since there were a few days where I could not even walk up stairs because my lungs would seize up instantly. My doctor told me to try exercising more in spite of me having a low BMI, being unusually active, and having asthma, since the drugs which are available for people with asthma mainly treat the symptoms. If you want to avoid needing them in the first place, increasing your stamina is the only fix.
Of course, before you can exercise at all, you need to either find effective medications, or exercises which you can manage without killing yourself, but I don’t understand your reaction to Molybdenumblue.
Tangentially, your symptoms do seem to match asthma well to me. I would recommend asking for tests next time you see a doctor.
Of course, before you can exercise at all, you need to either find effective medications, or exercises which you can manage without killing yourself, but I don’t understand your reaction to Molybdenumblue.
I think his comment came across as kind of snarky (“oh you should totally...”) and that might be why.
I think his comment came across as kind of snarky (“oh you should totally...”) and that might be why.
Oh dang girl, I’ve sent you PM’s about how I use my vagina and you still call me he? I think I just won the least feminine woman on the internet award or something.
Heh, I wasn’t insulted. I got into the habit of keeping my sex on the down low when I was playing WoW (because being conspicuously female gets you a lot of bad/icky attention and is only worth it if you play it for special treatment, which I didn’t want), so I don’t tend to spray a lot of girly text-pheromones around. That’s all I meant when I said I won the least feminine woman on the internet award. Definitely didn’t mean you were unfeminine, or un-feminist, or anything like that.
Whoops. I think more to the point, I don’t always remember who has what username. I’m a bit that way in real life too: I don’t always pay attention to who I’m talking to when I get onto discussing ideas. (I’m not sure if you meant “feminist” or “feminine” but I’m neither so that’s fine.)
I understand both of their arguments, but the emotions involved are incomprehensible...
I suppose I would have said nearly the same thing in Moly’s position, and would not have predicted that I was being offensive. It would be helpful to be able to empathize with peoples emotions, but I am apparently horrible at it.
My doctor told me to try exercising more in spite of me having a low BMI, being unusually active, and having asthma, since the drugs which are available for people with asthma mainly treat the symptoms. If you want to avoid needing them in the first place, increasing your stamina is the only fix.
I was diagnosed with asthma just over a year ago. (The only symptom I’ve ever had is that in winter when I get a cold, I cough for the rest of the year unless I go on steroid inhalers). My lung capacity dropped by 22% when I did the methacholine challenge test (inhaling an irritating chemical) but I barely noticed it. This is probably related to the fact that I started swimming competitively when I was eight, and my lung capacity is already much higher than the average for someone my height and weight. (I don’t know if I could have reached this point if my asthma had started before I began swimming, though. Ironically enough, I’m pretty sure my current asthma is caused by too mcch chlorine exposure over the years, and I’m considering taking a summer off from lifeguarding to “detox” myself enough that I can test negative on the asthma test.)
Me too. I get cold easily if I stay still, but even just walking briskly makes me start to sweat. I think this is one of those thigns that you can train with practice; the more you exercise, forcing your body to overheat, the better your body gets at efficiently disposing of the excess. Also getting used to it probably makes it less unpleasant… That being said, I hate exercising indoors on a treadmill or elliptical for precisely this reason. Biking outside is great in the spring and fall months, when my wonky thermostat actually works to my advantage and makes it possible to bike across the city on a −5 C morning.
Also, have you ever tried swimming for exercise? It has the benefits of burning a lot of calories without bringing your heart rate (and out-of-breath-ness) up as high as the same intensity exercise on land. Also if you hate the feeling of being sweaty, which I do, a nice temperature-controlled pool helps a lot. My brother’s asthma has improved drastically since he started swimming competitively...swimming does a lot more for your lung capacity and breath control than other activities of the same intensity.
Swimming in a temp-controlled pool is great on the overheating front and is the only known form of exercise where I am not bothered by sweating. However, pools tend to be either (A) indoors, with stiflingly enclosed humid environments where I can’t breathe comfortably (I sometimes have to stick my head out from behind the shower curtain when I’m in the shower, for reference, and didn’t like being in indoor pool environments even when I was kid and didn’t have clinically significant breathing issues) or (B) outdoors, and open only during the day, such that I have to either wear texturally-obnoxious sunscreen or crisp up like a rasher of bacon. Arranging to swim is also inconvenient—it requires changes to my state of dress, a new venue, etc, twice. Typically it is expensive, in a way that going for a walk is not.
None of these difficulties are individually insurmountable, and if all I had to do was one of living with humidity, or putting on sunscreen, or changing clothes twice, or going to a new location twice, or paying money, I’d get over it. I imagine that I’d swim a lot if I had a pool at my home, which would reduce it to a clothes-changing inconvenience if I swam in the dark. But I do not have a pool at my home.
Incidentally, I took a pulmonary function test a couple weeks ago. The guy who administered it wasn’t technically qualified to say so, but he thought everything looked normal, and if my GP agrees, the next step is probably to assume I have a heart problem.
Incidentally, I took a pulmonary function test a couple weeks ago. The guy who administered it wasn’t technically qualified to say so, but he thought everything looked normal, and if my GP agrees, the next step is probably to assume I have a heart problem.
Agreed that swimming is massively inconvenient, which is one reason I’m trying to start running more...once I move on from working at a pool, it’ll be even less convenient since I won’t already be there in a bathing suit anyway, or be able to swim for free. (There is one interesting thing I’ve noticed about myself...I find it massively inconvenient to take a shower at home, whether before bed or first thing in the morning...for the most part I only shower after teaching swimming lessons or after a workout. This is ok because I’m in the pool nearly every day for some reason or other.)
I wish I had a pool at my home...oh I can dream.
Just a heads-up: pool ventilation varies. I’ve swum at several dozen different pools over my life, and some were awful, with the air hotter than the water and ridiculously humid. Some were excellent. Any big Olympic-size pool that hosts competitions tends to have better ventilation than your local neighborhood pool for kids and old ladies. Saltwater pools tend to have better air quality too, if there are any near your home. And lakes and rivers in summer are my favorite, although I have pretty low squeamishness and I know some people are more bothered by weeds, mud, fish etc.
Incidentally, I took a pulmonary function test a couple weeks ago. The guy who administered it wasn’t technically qualified to say so, but he thought everything looked normal, and if my GP agrees, the next step is probably to assume I have a heart problem.
Also, have you ever tried swimming for exercise? It has the benefits of burning a lot of calories without bringing your heart rate (and out-of-breath-ness) up as high as the same intensity exercise on land.
My experience with swimming is that simply being in water strains your lungs more (as you have to displace water to inhale air). Simply going to the pool and talking to someone while in up to your neck is probably good lung training, but until she can do that comfortably and without attacks I would recommend against trying laps or other sort of exercise.
My experience with swimming is that simply being in water strains your lungs more (as you have to displace water to inhale air).
That’s probably where the long-term benefits of lung capacity come from. Aquafit (where your head doesn’t go underwater) is pretty low-intensity compared to on-land aerobics, and you don’t overheat so much so it might be preferable for her. On the other hand, something like breaststroke is a good way of training yourself to breathe rhythmically while exercising.
Do the twitch go at some harmonic with your heart beat? I have had something similar with eyelids, leg, neck, and other places twitch with the blood flow. More likely to happen after prolonged stress for myself. The solution for myself is to relax my muscles and modify my heart rate, usually with deep breaths.
The twitching is an erratic rhythm. I’ll take my pulse next time one happens and see if it’s even a little connected to my heartbeat, but I suspect not.
Agreed that the doctor telling you to exercise, at this point, is unhelpful and kind of a stupid thing to say. And I don’t think exercise would solve your problem. Not exercising is a risk factor for all sorts of other problems later in life, especially if it’s in combination with a not-very-healthy diet...but that’s a reason to look for solutions to your lung problem, not a reason for doctors to tell you that exercising will solve your lung problem.
Is it ok if I post this thread to my livejournal? A fair number of my readers are smart people with health problems, and they may either have heard of something like what you’ve got or may have information about the reliability of common tests for possible causes.
I’d probably make an arithmetic mistake anyway. I can barely compose a mathematically accurate D&D character, and I’m way more motivated there than here.
This isn’t a very good example. Making D&D characters that fit the rules can be surprisingly tricky. There’ s just a lot of data to keep track of and lots of little corner case rules.
A mostly solved problem. Although this doesn’t quite handle all possible combinations of those add on books. Like the one which can be gamed to create what amounts to adamantium nano-bots (which are actually fairly reasonable if you think about what a rational individual would do given the physics but are nevertheless not quite intended).
Manual arithmetic and rules knowledge would also be required to work out exactly how much damage can be done when using a locate spell to utterly obliterate nearly everything on an entire continent.
There is an additional constraint which you are missing here. Training pilots is expensive, and the military wants to recoup that cost by sending everyone they bother to train out on a certain number of missions. They weren’t going to just run two rounds and then decide the war’s over; rather, the plan was to keep sending out bombing raids until they run out of pilots, whether death or retirement, and then train some more pilots so they can continue bombing Japan.
That’s at best an argument against the political viability of iterated straw drawing due to general irrationality, not against the rationality of iterated straw drawing itself. The pilots are definitely worse of when everyone is sent to their death. If the pilots opinions don’t matter sending them all to their death is the best option since it saves training costs. If a compromise acceptable to the pilots need to be found then iterated straw drawing is the best option for everyone for any possible mission count and any gived cadre size, provided the pilots can make the necessary precommitment. Command might possibly reject this compromise due to some pilots appearing to be freeloading, but would act irrationally in doing so.
Of course doing the straw drawing at an earlier stage and optimizing training for whether they are going to be sent to their death or not would be even more efficient, but that level of precommitment seems less psychologically plausible.
The problem is, pilots aren’t optimizing for overall survival. Somebody who wanted to live to see the end of the war, at all costs, could’ve just faked some medical problem and gotten themselves a desk job. The perceived-reproductive-fitness boost associated with being a member of the flight crew is contingent on actually flying (and making it back alive, of course). In simpler terms, nobody gets laid by drawing the long straw.
That’s your third completely unconnected argument, and this one doesn’t make Japan and return missions assuming viability of straw drawing rational either. Even if the pilots are rationally maximizing some combination of survival and military glory that doesn’t mean Japan bombing and return missions with most of the load devoted to fuel are an efficient way to gain it. You could have all pilots volunteering to be part of the draw for one way missions and those who draw long being reassigned to Europe or whereever they can earn glory more fuel efficiently.
You’re assuming that straw drawing is viable. I’m trying to show why it wasn’t.
You seem to have a theory, based on that invalid assumption, about what will and will not work to motivate people to take risks. Does that theory make any useful predictions in this case?
You’re assuming that straw drawing is viable. I’m trying to show why it wasn’t.
Then you are wasting everyones time, we already know that it wasn’t viable. It was suggested and rejected. The whole discussion was about a) what would be needed to make viable (e. g. sufficiently high rationality level and sufficiently strong precommitment) and b) whether it would be the rational thing to do given the requirements.
You seem to have a theory, based on that invalid assumption, about what will and will not work to motivate people to take risks. Does that theory make any useful predictions in this case?
No. I was taking your model of what will and will not work to motivate people to take risks and demonstrating that your conclusion did not follow from it.
You’re still not understanding the math here. If we’re looking at this from the military’s perspective, it’s also a win, because an identical quantity of bombs dropped come at the cost of 2 flight crews (and planes) rather than 3.
You had a mistake in your mathematical intuition. That’s OK, it happens to all of us here. The best thing is to admit it. (NB: it’s your argument that’s deeply flawed and not the conclusion, so raising other reasons why this would be a bad policy is irrelevant at the moment.)
I still can’t figure this out. Faced with the choice between leaving, having learned nothing, and continuing to lose karma for every damn post I make, what does your model recommend?
Say you start out with 100 pilots. You have two options:
Send all 100 pilots to Japan with full fuel tanks. 25 make it back alive.
Send 50 pilots to Japan with twice as many bombs. 0 make it back, but 50 are still alive.
the military wants to recoup that cost by sending everyone they bother to train out on a certain number of missions.
No, the military just wants to accomplish its missions. If more pilots are alive after each mission, it means more pilots available for future missions.
When the general case seems confusing, it’s often helpful to work out a specific example.
Let’s say that there are 40 targets that need to be bombed, and each plane can carry 10 bombs normally, or 20 bombs if it doesn’t carry fuel for the return trip. We’ll assume for simplicity that half of the bombs loaded on a plane will find their targets (accounting for misses, duds and planes shot down before they’re finished bombing).
Then, with the normal scheme, it would take eight flights on average to bomb the forty targets, and six of those planes would go down. If instead the planes were loaded with extra bombs instead of return fuel, it would take only four such flights (all of which would of course go down).
If there are eight flight crews to begin with, drawing straws for the doomed flights gives you a 50% chance of surviving, whereas the normal procedure leaves you only a 25% chance. If those are all the missions, it’s clearly rational to prefer the lottery system to the normal one. (If instead the missions are going to continue indefinitely, of course, you’re doomed with probability 1 either way.) And of course the military brass would be happy to achieve a given objective with only 2⁄3 the usual losses.
The difficulty with thinking in terms of “half-lives of danger” is that it’s the reciprocal of your probability of survival, so if you try and treat them as simple disutilities, you’ll run into problems. (For instance, if you’re facing a coinflip between dangerous activities A and B, where A consists of one half-life of danger and B consists of five half-lives, your current predicament is not equivalent to the “average value” of three half-lives of danger.)
Let’s say that there are 40 targets that need to be bombed, and each plane can carry 10 bombs normally, or 20 bombs if it doesn’t carry fuel for the return trip. We’ll assume for simplicity that half of the bombs loaded on a plane will find their targets
What if there’s a hidden variable? Say, a newly-trained flight crew has skill of 1, 2, or 3 with equal probability. On any given mission, each bomb has a 10% chance, multiplied by the crew’s skill, to hit it’s target, and then at mission’s end, assuming adequate fuel, the crew has the same chance of returning alive. If they do so, skill increases by one, to a maximum of seven.
Furthermore, let’s say the military has a very long but finite list of targets to bomb, and is mainly concerned with doing so cost-effectively. Building a new plane and training the crew for it costs 10 resources, and then sending them out on a mission costs resources equal to the number of previous missions that specific crew has been sent on, due to medical care, pensions (even if the crew dies, there are certain obligations to any surviving relatives), mechanical repairs and maintenance, etc.
OK then. You can of course add additional factors to the basic model, and some of these will mitigate or even overwhelm the original effect. No problem with that. However, your original mathematical intuition about the basic model was mistaken, and that’s what I was talking to you about.
In general: let’s say someone proposes a simple mathematical model X for phenomenon Y, and the model gives you conclusion Z.
It’s always a complicated matter whether X is really a good enough model of Y in the relevant way, and so there’s a lot of leeway granted on whether Z should actually be drawn from Y.
However, it’s a simple mathematical fact whether Z should be drawn from X or not, and so a reply that gets the workings of X wrong is going to receive vigorous criticism.
Let’s say somebody who flies out with extra bombs instead of fuel has an overall 0.1% chance of making it back alive through some heroic exploit. Under the existing system, with 25% survival, you’re asking every pilot to face two half-lives worth of danger per mission. With extra bombs, that’s half as many missions, but each mission involves ten half-lives worth of danger. Is it really all that rational to put the pilots in general in five times as much danger for the same results? After all, drawing the long straw doesn’t mean you’re off the hook. Everybody’s going to have to fly a mission sooner or later.
Thinking in terms of “half-lives of danger” is your problem here; you’re looking at the reciprocal of the relevant quantity, and you shouldn’t try and treat those linearly. Instead, try and maximize your probability of survival.
It’s the same trap that people fall into with the question “if you want to average 40 mph on a trip, and you averaged 20 mph for the first half of the route, how fast do you have to go on the second half of the route?”
How do you answer this question?
Edit: MBlume kindly explained offsite before the offspring comments were posted. Er, sorry to have wasted more people’s time than I needed.
It’s still an interesting exercise to try to come up with the most intuitive explanation. One way to do it is to start by specifying a distance. Making the problem more concrete can sometimes get you away from the eye-glazing algebra, though of course then you need to go back and check that your solution generalizes.
A good distance to assign is 40 miles for the whole trip. You’ve gone 20 mph for the first half of the trip, which means that you traveled for an hour and traveled 20 miles. In order for your average speed to be 40 mph you need to travel the whole 40 miles in one hour. But you’ve already traveled for an hour! So—it’s too late! You’ve already failed.
Yes, that’s roughly how MBlume explained it (edited for concision and punctuation):
If that’s an actual chat record, I’m getting old for this world. … okay, on a third read-through, I’m starting to comprehend the rhythm and lingo.
The original had more line breaks and less punctuation, but it’s real—what do you mean?
It felt like I was following, say for analogy, a discussion among filipinos who were switching back and forth between English and Tagalog. But re-reading it twice I started to get the flow and terms. E.g. “nodnod” was opaque initially.
Nowadays young people are all like
Yes, that movie is a nice example of science fiction which deliberately makes up new words (so I presume) to give the viewer that fish out of water “it’s the future” feeling. Star Trek does something like that which I think is called technobabble, which is also deliberately incomprehensible with a sciency twist. I get much the same feeling when I watch certain popular shows from English- but not American-speaking places, where people combine unknown references, unknown words, and pronunciation which I have to struggle to unravel.
Happily, in all cases the simple act of patiently familiarizing myself by repeated viewing works well to bring me up to speed, though I personally have never gone as far as learning Klingon.
If I remember correctly, it’s a blend of English, Russian, and Latin.
I guess it is rather bizarre. But most of the unusual conventions on IRC and other chat services are in order to make it more like a face to face conversation. They generally either allow you to narrate yourself from a third person perspective, or speed up common interactions that take much longer to type than they do in real life.
Although “nodnod” seems unusually nonsensical, since it takes longer to type than “yes”. I cannot say I have seen that used before.
I think it’s actually pretty close to normal English for a chat log.
I don’t doubt it. That’s why I said that I felt that I was getting old for the world. The unusual, out of place thing is me. I’m assuming that the chat log is typical.
Suppose the total trip is a distance d.
So if your average speed is 40 (mph), your total time is d/40.
You have already travelled half the distance at speed 20 (mph), so that took time (d/2)/20 = d/40. Your time left to complete the trip is your total time minus the time spent so far: d/40 - d/40 = 0. In this time you have to travel the remaining distance d/2, so you have travel at a speed (d/2)/0 = infinity, which means it is impossible to actually do.
Let t1 be the time taken to drive the first half of the route.
Let t2 be the time taken to drive the second half.
Let d1 be the distance traveled in the first half.
Let d2 be the distance traveled in the second half.
Let x be what we want to know (namely, the average speed during the second half of the route).
Then the following relations hold:
40 (t1 + t2) = d1 d2.
20 * t1 = d1.
x * t2 = d2.
d1 = d2.
Use algebra to solve for x.
To average 40 mph requires completing the trip in a certain amount of time, and even without doing any algebra, I notice that you will have used all of the available time just completing the first half of the trip, so you’re speed would have to be infinitely fast during the second half.
I am pretty confident in that conclusion, but a little algebra will increase my confidence, so let us calculate as follows: the time you have to do the trip = t1 + t2 = d1 / 40 + d2 / 40, which (since d1 = d2) equals d1 / 20, but (by equation 2) d1 / 20 equals t1, so t2 must be zero.
I expect a high probability of this explanation being completely useless to someone who professes being bad at math. Their eyes are likely to glaze over before the half way point and the second half isn’t infinitely accessible either.
I already had the problem explained to me before I saw the grandparent, but I think you’re right—I might have been able to puzzle it out, but it’d have been work.
Can’t resist the urge to chime in here...
I first started long-distance running when I was 20 years old. Up until that moment I hated everything about running, especially the sharp pain in my lungs whenever I ran more than 50 meters or so. But as soon as I gave it a serious try, the pain went away completely after about a week of morning runs, and from that day it never came back. Now I love running. And sometime later I found out that long-distance running is one of the few areas where humans can beat pretty much every animal out there. Something we’re naturally good at.
Another such area is intelligence.
I know that you are an intelligent person, whatever your other flaws. And I don’t completely understand what can stop an intelligent person from solving trivial puzzles such as orthonormal’s original question. Could your perception of “it’d be work” be the mental equivalent of lung pain that unexperienced runners have? Something that would just go away forever if you gave it a week of effort?
Well, in the department of actual running, I have some kind of mysterious lung issue that means I need to gasp for air a lot even when I’m sitting still and have been for hours and it only gets worse if I try to do exercise more strenuous than a leisurely walk. (Armchair diagnoses appreciated, incidentally—so far I’ve stumped multiple doctors and new Google keywords are good.)
Here is something like the thought process that goes through my head when I encounter a problem of this approximate type:
I know what all those words mean. I could come up with a toy scenario and see what’s interesting about this problem, that someone bothered to bring it up.
It might be the sort of question where coming up with one toy scenario doesn’t answer it because for some reason it doesn’t generalize. Like it could have to do with the distance. I don’t want to come up with five different distances and work it out for all of them. I’d probably make an arithmetic mistake anyway. I can barely compose a mathematically accurate D&D character, and I’m way more motivated there than here. I’m not interested enough in this to do it in a calculator and then re-read the ticker tape. My eyes are swimming just thinking about it.
And because I’m not good at this, I would be reasonably likely to get it wrong, and then, no matter how much time I’d put into it myself, I would need to ask someone. I could get help if I asked. I am cute and friendly and there are helpful people around. I could get help even if I didn’t work on it myself. That would be faster, and then I’d know the answer, and I have to ask anyway, so why not just ask? Why not save the work, and not risk wasting a lot of time on getting a wrong answer and having to stare at all those numbers?
Record yourself (audio and video) during one of your attacks and I’ll have a much better idea. Right now, it’s extremely hard to tell from your description. Obviously, actually listening to you with a stethoscope and being able to perform a few tests would help me even more, of course.
By “attack” do you mean “one of the hundreds of occasions throughout an average day where I attempt to take an especially deep breath to satisfy my customary air hunger” or do you mean “run around until you collapse, gasping, and record that”?
The latter. But wait, you only have attacks when you run?
Running, biking, walking too fast up a hill, jumping on a trampoline, playing DDR.
Ok, but those are all exercise. Do you ever get attacks from cold, from allergens, from waking up in the middle of the night, from fear, from pain, from eating too much before bedtime?
Cold weather can make getting my deep breaths uncomfortable, but doesn’t seem to make me need more of them. I’m not allergic to anything except mushrooms (and that causes nausea, not breathing problems). I’ve never woken up in the middle of the night (that I know of) with breathing problems. I sometimes breathe oddly when afraid/in pain, but it doesn’t seem related. Eating too much at bedtime doesn’t do anything that eating too much at other times doesn’t.
Ok, so a video c audio of you exercising (or aftermath) would be helpful. As I said, not as helpful as seeing you in person.
I’ll try to remember to do this next time, and may induce it deliberately if my next doctor visit is disappointing in this regard.
Sorry for deleting my comment. I’ve been doing this a lot lately—I write something and then notice that it’s stupid for one reason or another. (In this case it was the armchair diagnosing/other-optimizing.) Didn’t think you’d react so fast.
It’s okay. (I hope my thought process is interesting anyway.)
Well your last paragraph was interesting in a way. In fact I don’t understand it. The point of a puzzle is to stretch and work out your brain, not arrive at an answer asap. If you have a bus full of hostages whose fate depends on an arithmetical problem, it’s indeed wiser to ask someone else. But such situations don’t occur often. In fact I sometimes explicitly ask other people to avoid giving me any hints because I want to solve the puzzle myself. Asking for help is analogous to taking the bus instead of your morning run :-)
But well, I guess if you don’t enjoy puzzles already, then saying things like “c’mon jump in, the water’s fine” isn’t going to influence you much. Some things you really have to try before you can see the fun contained within. I think most things I enjoy in life fall in this category...
I hate being frustrated. It happens to me very easily. I hate not knowing the endings to stories, I hate not knowing what I’m getting for my birthday, and the only way I can not hate not knowing the answers to math problems is by not giving a flying fuck about them at all—which isn’t conducive to expending effort on solving them. I’ve generalized the “stop giving a fuck” self-defense strategy to other hatreds-of-not-knowing stuff, mostly to discourage people from teasing me with this neurosis. I believe that other people can enjoy various forms of not-knowing-stuff, or fail to hate it enough to override some competing desire to achieve knowledge on their own. But I don’t.
So basically, I looked at that math problem, sort of cared about knowing the answer, and asked. I got an answer (actually, several) which were quick enough to suit me. If the only way I could have learned the answer were to work it out for myself—or sit through ten minutes of algebra lessons or something—then I would have defensively ceased to care, instead.
Once I know the answer—in this case, that after having gone halfway at 20mph, you need to teleport to get to point B in time—then I can tolerate some further discussion of the scenario or the underlying math (although not arbitrary amounts). This is much the same as how, when I know that character X and character Y in some story eventually get together (or find the MacGuffin, or die, or whatever major plot item), I can often put up with extended periods of wondering exactly when and how.
I’ve found in the past that I remember the right answer better if I can guess it first and then get confirmation. It doesn’t help when I guess wrong, but when I guess right it’s a win.
Has the lung issue been a problem for your whole life? Is it better at some times and worse at others?
I don’t have a theory, but this seems like a reasonable starting point.
The lung thing has gone on for several years; I have a memory that doesn’t make sense without it that has to have taken place in fall 2006. I don’t remember exactly when it started but I have not always had it. (I suspect it began sometime after I started taking iron to treat my anemia, since no one ever connected the two; that would’ve been some months after I turned 17, so, late 2005-early 2006).
It does vary day to day and hour to hour, plus with what I’m doing (walking excessively briskly, or jumping around, or otherwise being active, makes it act up—it was outright crippling on one occasion last summer when I tried to bike a few blocks; I had to pull over and sit on the sidewalk for a while and then verrrrry carefully bike back, walking the thing up hills and only riding on levels and downhill.) There is an overall trend of worsening from year to year.
Who is ‘no one’ and which two did they fail to connect? Why do you say ‘since’?
I’m not a doctor. But it sure sounds to me that your blood is just not carrying enough oxygen to support vigorous exercise. Which is by definition ‘anemia’. Which comes in various forms, the most common of which can be treated by iron supplements, but the most serious of which have other causes and treatments. Just from what I read on the web, my guess would be you have ‘pernicious anemia’.
I would strongly advise going to a doctor again, and asking for blood tests. Be sure the doctor is informed about any ways in which your diet is unusual. Good luck.
“No one” is a couple of internists, my dad and my uncle (both doctors), and various random people I mentioned it to. What I mean is that people who know I used to be anemic and that I now have this dyspnea problem have never asked “I wonder if you still have [anemia-related subcondition] and that’s causing the dyspnea?”
The iron pills working was confirmed with a blood test. Before I took iron pills, my readings on some relevant feature of my blood were so low that I ought to have been fainting on a regular basis; after they were in normal range and I’ve been allowed to give blood several times since.
Asthma/reactive airway disease seems like the obvious thing here, so has that been ruled out? Did they have you blow into a thing to measure whether you were breathing a normal volume of air (spirometry)?
I have never had to blow into a thing. Since I have consulted plural doctors about this, I’m not sure why none of them would have thought of athsma if that were consistent with my symptoms. Why might that be?
Asthma usually shows up in childhood, not at 17, and maybe some of the doctors you saw assumed that previous doctors would have checked out the possibility of asthma already. The definitive test for asthma is called a methacholine challenge; basically you inhale a chemical that irritates your lungs, and if you’re asthma-prone then you have trouble breathing (there is no physical activity involved).
It probably isn’t a heart issue if you haven’t always had it...those are usually congenital...but I could be wrong. (Also not a doctor). But it sounds very debilitating, and worth fixing.
That is troubling. Even if it isn’t asthma it is definitely something to do with the lungs that influences breathing. Measurement of breathing capabilities should be one of the first things they do!
Honestly? No idea. Nursing student here, in no way a doctor. But if I were you I’d go to a doctor and describe my symptoms and say “Could I have asthma?” I’m thinking most likely outcome is they give you some meds to try, which could be a good thing, you know? Certainly before you go after any of the zebras you’ll get by Googling around.
My other thought is it could even be a heart issue, if your lungs check out. I’m kind of..surprised...that no one is more concerned about an apparently healthy young person being unable to breathe, so I’m guessing your oxygen saturation isn’t dropping to scary levels or anything.
Well, I’ve never passed out, and I tend not to take much exercise that this is interfering with, and doctors in general like to say that absolutely everything that could possibly be wrong with me will be fixed with exercise, which advice I ignore, which can then go on indefinitely “explaining” my problem. (I went in with little muscle twitches in my legs and eyelids once—I still get those, still don’t know what they are—doctor says, “Consider getting more exercise”. Exercise my eyelids, right? I’m not blinking enough?)
Clearly that is not what they are suggesting. Generalised exercise does clear up some such twitches. It may not in your case and it is even conceivable that you could die trying. But regardless the exercise suggestion in response to that complaint is not absurd or a valid target of mockery.
If this were the only thing doctors bizarrely said I should exercise for, I could shrug and say that maybe there is a mystical eyelid-exercise connection.
But I get told this a lot (mysterious lumps on your back? Exercise! Left foot makes a crunchy noise when you move it like so? Consider the benefits of exercise. You get lots of headaches? Try exercising! Sometimes the palms of your hands swell up for no reason? I recommend more exercise. You keep getting ingrown toenails? That may go away with enough exercise. If you exercise, you can’t breathe? Maybe you should fix that with exercise.)
I’m pretty sure that they’re coming up with this too quickly, for too many things, which means I’m suspicious of each instance of advice to get more exercise (for a specific problem; I’m tired of, but not suspicious of, the advice that it would just be a good idea in general.) I think it is more likely that they are saying this because I’m fat, not because it’s related to the problems I go in with. Often I am not even asked how much I exercise before a health professional says I need to do more of it.
Perhaps more importantly it sounds like they come up with ‘exercise’ then stop. For many things exercise will help, even if only indirectly, but it certainly isn’t the primary treatment. Sure, exercise is great for asthma, but so are steroids—and sometimes the former isn’t enough. Likewise for blood pressure and heart disease. Come to think of it exercise is great for the symptoms of being a chronic smoker… but if the doctor stopped at ‘exercise more’ without going on to ‘stop smoking dumbass!’ there would be a problem!
Apart from being interpersonally rude that doesn’t seem to reflect well on their medical competence. There is a relationship between exercise and fat storage but it isn’t all that strong. Doctors aren’t supposed to be going along with popular stereotypes!
I’m reminded of the day I was running my first marathon. I was up to the 30km mark and starting to feel it. Then along beside me comes a guy built like a 44 gallon drum on legs. He was puffing away but looked like he was ready to run another 30km then maybe do it again after lunch. While I was slowing down with fatigue and complete glycogen depletion he was accelerating. That rather completely destroyed any preconceptions I may have had that people with a high bodyfat ratio must not exercise.
It’s scary, but I have no problems believing that. Along similar lines my father’s doctor (well, former doctor) concluded from his high cholesterol on his bloodwork that he clearly eats too much fast food and needs to cut back on the KFC. Where was that doctor when the studies were published regarding just what the limits of the influence of diet on cholesterol are? Even worse is my mother’s (former) doctor insisting that she is a long term alcoholic and needs help, despite her protestation to the contrary. She hasn’t consumed a drop of alcohol in her entire life. The high indicators of liver strain are a known side effect of the rather potent medication she takes for neuropathic pain.
I often wonder just how some of these people go through a decade of training and still end up clueless.
I have a notion that sleep deficiency during that training damages their mental flexibility.
I’ll track it down if you care, but I just read something which claims that twitching eyelids are a minor side effect of stress. This does seem to be true for me.
For some people, exercise lowers their stress level, so the doctor’s advice isn’t entirely crazy.
On the other hand, casual surveying has turned up a shockingly consistent result that only about 20% of doctors listen and think. This implies that you need to be persistent if you need a diagnosis for something that’s even a little weird.
Even fairly easy problems like celiac can take a surprisingly long time to get diagnosed.
I’m not under stress most of the time.
Exercise raises my stress level. (One time, exactly one, in my entire life, I felt sort of high after getting some exercise. I thought it was cool and tried to reproduce it and couldn’t.) Even if I’m just walking, gently enough that my lungs don’t care, it makes my feet hurt and the rest of me too hot until all I want to do is fling myself into a frigid shower and collapse until I’m cold enough to believe that it’s safe to leave the water. (I routinely arrange to be too cold, because definitely being too cold is safer and more comfortable than maybe being too hot.)
Oh, you totally should get more exercise, and they are right to tell you that, although maybe they would have better luck if they came across as more helpful. But I’m a slug too and I can breathe ok; I just can’t run very far. I still vote asthma.
No, I should bloody well not get more exercise, because when I do, I can’t fucking breathe. Understood?
(Also I overheat, really easily.)
Walk. Start slow. Exercise indoors. You know the answers here. Advanced COPD patients still need to get out of bed and do physical therapy.
Sorry I made you mad, of course, but it doesn’t change anything.
Edit: downvote wasn’t me
Alicorn has implied that she isn’t completely sedentary or bedridden—she goes out walking, and sometimes gets seriously out of breath.
Is there any reason to think that more exercise will be good for her?
How much do you actually know about the subject?
More exercise is generally good for most people, which is one reason. Aerobic exercise tends to increase aerobic capacity, and decreases the risk of plenty of chronic diseases.
Alicorn admits she doesn’t get much exercise, so she’s clearly not in the tail of people who already exercise strenuously enough that more exercise would be harmful. Light exercise like I suggested is very unlikely to do any harm, and could very well even help her symptoms by improving her endurance.
By way of clarification, I do not intend to blame Alicorn for her symptoms. I understand why she might feel that way, and I regret that she has been made to feel dismissed in the past. My suggestion that she see a doctor and ask about asthma is much more urgent and important, so I want to reemphasize it rather than get stuck on the question of exercise.
Not exercising is a problem for anybody regardless of whether they have a breathing problem or not. It raises your chances of obesity, which later on can lead to lots of nasty consequences, and I think sedentary people show an increase in certain chronic diseases (heart disease for sure, type 2 diabetes possibly but I don’t remember for sure) regardless of weight. In that sense, more exercise would be good for Alicorn.
That being said, I think it’s misleading to say it would directly fix her mystery respiratory problem. (Even if it turns out to be asthma...exercise doesn’t cure asthma and can even trigger it for certain people). It might improve the symptoms in the long run. It might not. There might be another way to improve the situation enough that she can exercise.
Recent studies have suggested that obesity causes lack of exercise, rather than the other way around, and that’s why we see the correlation.
Got a cite? (Not that I disbelieve you, I find it highly plausible—I’m just curious.)
here is an abstract for a longitudinal study that suggested childhood obesity leads to lack of exercise and not the reverse.
I feel certain I’ve seen reference to a more recent study involving adults, but I haven’t turned it up yet.
I’m half convinced. However, I keep reading that inactivity is unhealthy regardless of whether it is fattening. Therefore fat people have good reason to try to resist the tendency to inactivity induced in them by their fatness.
So: why are fat people inactive? My only tentative guess is that it is difficult for them to move their bodies, and they respond to the difficulty by moving less. This suggests the following possible remedy: strength training. With stronger muscles, your body feels like less of a burden, and so you are more likely to move around.
Very plausible. Also, fear and embarrassment could be factors. Several of my heavier friends have told me that they don’t like to go to the gym because they feel self-conscious surrounded by fitter people. This is probably also true of, for example, jogging in public; they are afraid of people watching them and judging them (“Look at that fat guy/girl trying to run!”).
Yes, this was the basis for a Jerry Seinfeld comedy routine: “We need to have a pre-gym, a gym-before-the-gym. A place where you can get yourself fit enough to be comfortable going to the regular gym.” (And this actually isn’t far from the reason for the success of the franchise Curves.)
I was strongly voted up a while back for making the above point and then suggesting we have the analog website for LessWrong—a place where people can learn and discuss this stuff without being intimindated by those who know more.
If only the users of Curves graduated to regular gyms more frequently...
The study (which needs significant followup to create usable results) could have a number of interpretations, including:
*conclusions not fully supported by the data
*obesity leads to less enjoyment of motion
*obesity leads to fewer social opportunities to engage in sports
*low socio-economic status leads to obesity and to inactivity (due to insufficient access to parks, to parents who force you out of the house, etc).
*People don’t record their activity levels every day, so their estimates are colored more by measurable factors (body weight) than by unmeasurable ones (how much they actually moved).
I’d hesitate to read too much into this study.
Interesting. Thanks for the heads-up. I will research that now.
Whereas I dropped 13kg very quickly not by more exercise, but by a change in diet.
The whole area is a minefield of YMMV …
Valid point. I’ve read that for sedentary people, starting an exercise regime is a poor way to lose weight. I still think it’s an excellent way not to gain weight in the first place...children who active, who remain active as teenagers and young adults (and don’t grossly overeat) probably won’t put on the weight in the first place. I did an energy-expenditure study that showed I burn nearly 3000 calories a day, mainly because I can maintain an ‘intense’ level of exercise for an hour or more, whereas someone who is unfit and overweight already probably can’t and so wouldn’t burn nearly as many calories. Muscle mass also burns more calories at rest than fat tissue, so that someone at a high level of fitness can eat more even on days when they don’t exercise.
The moral of the story: I’m going to put my kids in one physical activity after another (like my parents did with my siblings and myself) until they find one they can stick with, and I’m going to try to keep it a part of family life. After all, it takes far less willpower to maintain a lifelong habit than to start a new regime once you start putting on weight.
That was harsh...
I was in exactly the same situation when I was 15 before I was diagnosed with asthma, probably worse since there were a few days where I could not even walk up stairs because my lungs would seize up instantly. My doctor told me to try exercising more in spite of me having a low BMI, being unusually active, and having asthma, since the drugs which are available for people with asthma mainly treat the symptoms. If you want to avoid needing them in the first place, increasing your stamina is the only fix.
Of course, before you can exercise at all, you need to either find effective medications, or exercises which you can manage without killing yourself, but I don’t understand your reaction to Molybdenumblue.
Tangentially, your symptoms do seem to match asthma well to me. I would recommend asking for tests next time you see a doctor.
I think his comment came across as kind of snarky (“oh you should totally...”) and that might be why.
Oh dang girl, I’ve sent you PM’s about how I use my vagina and you still call me he? I think I just won the least feminine woman on the internet award or something.
You are probably justified in being insulted that I completely forgot the vagina conversation was with you.
Heh, I wasn’t insulted. I got into the habit of keeping my sex on the down low when I was playing WoW (because being conspicuously female gets you a lot of bad/icky attention and is only worth it if you play it for special treatment, which I didn’t want), so I don’t tend to spray a lot of girly text-pheromones around. That’s all I meant when I said I won the least feminine woman on the internet award. Definitely didn’t mean you were unfeminine, or un-feminist, or anything like that.
Whoops. I think more to the point, I don’t always remember who has what username. I’m a bit that way in real life too: I don’t always pay attention to who I’m talking to when I get onto discussing ideas. (I’m not sure if you meant “feminist” or “feminine” but I’m neither so that’s fine.)
I understand both of their arguments, but the emotions involved are incomprehensible...
I suppose I would have said nearly the same thing in Moly’s position, and would not have predicted that I was being offensive. It would be helpful to be able to empathize with peoples emotions, but I am apparently horrible at it.
I was diagnosed with asthma just over a year ago. (The only symptom I’ve ever had is that in winter when I get a cold, I cough for the rest of the year unless I go on steroid inhalers). My lung capacity dropped by 22% when I did the methacholine challenge test (inhaling an irritating chemical) but I barely noticed it. This is probably related to the fact that I started swimming competitively when I was eight, and my lung capacity is already much higher than the average for someone my height and weight. (I don’t know if I could have reached this point if my asthma had started before I began swimming, though. Ironically enough, I’m pretty sure my current asthma is caused by too mcch chlorine exposure over the years, and I’m considering taking a summer off from lifeguarding to “detox” myself enough that I can test negative on the asthma test.)
Me too. I get cold easily if I stay still, but even just walking briskly makes me start to sweat. I think this is one of those thigns that you can train with practice; the more you exercise, forcing your body to overheat, the better your body gets at efficiently disposing of the excess. Also getting used to it probably makes it less unpleasant… That being said, I hate exercising indoors on a treadmill or elliptical for precisely this reason. Biking outside is great in the spring and fall months, when my wonky thermostat actually works to my advantage and makes it possible to bike across the city on a −5 C morning.
Also, have you ever tried swimming for exercise? It has the benefits of burning a lot of calories without bringing your heart rate (and out-of-breath-ness) up as high as the same intensity exercise on land. Also if you hate the feeling of being sweaty, which I do, a nice temperature-controlled pool helps a lot. My brother’s asthma has improved drastically since he started swimming competitively...swimming does a lot more for your lung capacity and breath control than other activities of the same intensity.
Swimming in a temp-controlled pool is great on the overheating front and is the only known form of exercise where I am not bothered by sweating. However, pools tend to be either (A) indoors, with stiflingly enclosed humid environments where I can’t breathe comfortably (I sometimes have to stick my head out from behind the shower curtain when I’m in the shower, for reference, and didn’t like being in indoor pool environments even when I was kid and didn’t have clinically significant breathing issues) or (B) outdoors, and open only during the day, such that I have to either wear texturally-obnoxious sunscreen or crisp up like a rasher of bacon. Arranging to swim is also inconvenient—it requires changes to my state of dress, a new venue, etc, twice. Typically it is expensive, in a way that going for a walk is not.
None of these difficulties are individually insurmountable, and if all I had to do was one of living with humidity, or putting on sunscreen, or changing clothes twice, or going to a new location twice, or paying money, I’d get over it. I imagine that I’d swim a lot if I had a pool at my home, which would reduce it to a clothes-changing inconvenience if I swam in the dark. But I do not have a pool at my home.
Incidentally, I took a pulmonary function test a couple weeks ago. The guy who administered it wasn’t technically qualified to say so, but he thought everything looked normal, and if my GP agrees, the next step is probably to assume I have a heart problem.
Thanks for the update.
Agreed that swimming is massively inconvenient, which is one reason I’m trying to start running more...once I move on from working at a pool, it’ll be even less convenient since I won’t already be there in a bathing suit anyway, or be able to swim for free. (There is one interesting thing I’ve noticed about myself...I find it massively inconvenient to take a shower at home, whether before bed or first thing in the morning...for the most part I only shower after teaching swimming lessons or after a workout. This is ok because I’m in the pool nearly every day for some reason or other.)
I wish I had a pool at my home...oh I can dream.
Just a heads-up: pool ventilation varies. I’ve swum at several dozen different pools over my life, and some were awful, with the air hotter than the water and ridiculously humid. Some were excellent. Any big Olympic-size pool that hosts competitions tends to have better ventilation than your local neighborhood pool for kids and old ladies. Saltwater pools tend to have better air quality too, if there are any near your home. And lakes and rivers in summer are my favorite, although I have pretty low squeamishness and I know some people are more bothered by weeds, mud, fish etc.
Best of luck, I hope they figure it out soon.
My experience with swimming is that simply being in water strains your lungs more (as you have to displace water to inhale air). Simply going to the pool and talking to someone while in up to your neck is probably good lung training, but until she can do that comfortably and without attacks I would recommend against trying laps or other sort of exercise.
That’s probably where the long-term benefits of lung capacity come from. Aquafit (where your head doesn’t go underwater) is pretty low-intensity compared to on-land aerobics, and you don’t overheat so much so it might be preferable for her. On the other hand, something like breaststroke is a good way of training yourself to breathe rhythmically while exercising.
Do the twitch go at some harmonic with your heart beat? I have had something similar with eyelids, leg, neck, and other places twitch with the blood flow. More likely to happen after prolonged stress for myself. The solution for myself is to relax my muscles and modify my heart rate, usually with deep breaths.
The twitching is an erratic rhythm. I’ll take my pulse next time one happens and see if it’s even a little connected to my heartbeat, but I suspect not.
Agreed that the doctor telling you to exercise, at this point, is unhelpful and kind of a stupid thing to say. And I don’t think exercise would solve your problem. Not exercising is a risk factor for all sorts of other problems later in life, especially if it’s in combination with a not-very-healthy diet...but that’s a reason to look for solutions to your lung problem, not a reason for doctors to tell you that exercising will solve your lung problem.
Was this an intentional pun, an unintentional pun, or a misspelling of “pleural”?
Unintentional pun, I suppose.
What hypotheses did the doctors check?
Is it ok if I post this thread to my livejournal? A fair number of my readers are smart people with health problems, and they may either have heard of something like what you’ve got or may have information about the reliability of common tests for possible causes.
I don’t know what the hypotheses were. I’ve had a chest x-ray, which I was told revealed nothing interesting.
Post away.
The link.
I’ve gotten a few replies so far. It’s likely that all the replies will arrive within three days.
Mayo clinic, from my very limit experience, can be quite thorough. You will at least have many eyes on the problem and the more the better.
They can offer finical asstance as well if they are not in network for your insurance. http://www.mayohealthsystem.org/mhs/live/locations/LM/pdf/FinancialAssistanceBrochure.pdf
This isn’t a very good example. Making D&D characters that fit the rules can be surprisingly tricky. There’ s just a lot of data to keep track of and lots of little corner case rules.
theonlysheet.com
A mostly solved problem. Although this doesn’t quite handle all possible combinations of those add on books. Like the one which can be gamed to create what amounts to adamantium nano-bots (which are actually fairly reasonable if you think about what a rational individual would do given the physics but are nevertheless not quite intended).
Manual arithmetic and rules knowledge would also be required to work out exactly how much damage can be done when using a locate spell to utterly obliterate nearly everything on an entire continent.
I have to agree that a shorter explanation with just words in it would be bettter for someone with significant aversive math conditioning.
It also doesn’t help the explanation when you make an error. That should be d1 + d2.
Acknowledged.
The probability of drawing the long straw twice in a row is four times as high as the probability of making it back twice in a row given 25% survival.
There is an additional constraint which you are missing here. Training pilots is expensive, and the military wants to recoup that cost by sending everyone they bother to train out on a certain number of missions. They weren’t going to just run two rounds and then decide the war’s over; rather, the plan was to keep sending out bombing raids until they run out of pilots, whether death or retirement, and then train some more pilots so they can continue bombing Japan.
That’s at best an argument against the political viability of iterated straw drawing due to general irrationality, not against the rationality of iterated straw drawing itself. The pilots are definitely worse of when everyone is sent to their death. If the pilots opinions don’t matter sending them all to their death is the best option since it saves training costs. If a compromise acceptable to the pilots need to be found then iterated straw drawing is the best option for everyone for any possible mission count and any gived cadre size, provided the pilots can make the necessary precommitment. Command might possibly reject this compromise due to some pilots appearing to be freeloading, but would act irrationally in doing so.
Of course doing the straw drawing at an earlier stage and optimizing training for whether they are going to be sent to their death or not would be even more efficient, but that level of precommitment seems less psychologically plausible.
The problem is, pilots aren’t optimizing for overall survival. Somebody who wanted to live to see the end of the war, at all costs, could’ve just faked some medical problem and gotten themselves a desk job. The perceived-reproductive-fitness boost associated with being a member of the flight crew is contingent on actually flying (and making it back alive, of course). In simpler terms, nobody gets laid by drawing the long straw.
That’s your third completely unconnected argument, and this one doesn’t make Japan and return missions assuming viability of straw drawing rational either. Even if the pilots are rationally maximizing some combination of survival and military glory that doesn’t mean Japan bombing and return missions with most of the load devoted to fuel are an efficient way to gain it. You could have all pilots volunteering to be part of the draw for one way missions and those who draw long being reassigned to Europe or whereever they can earn glory more fuel efficiently.
You’re assuming that straw drawing is viable. I’m trying to show why it wasn’t.
You seem to have a theory, based on that invalid assumption, about what will and will not work to motivate people to take risks. Does that theory make any useful predictions in this case?
Then you are wasting everyones time, we already know that it wasn’t viable. It was suggested and rejected. The whole discussion was about a) what would be needed to make viable (e. g. sufficiently high rationality level and sufficiently strong precommitment) and b) whether it would be the rational thing to do given the requirements.
No. I was taking your model of what will and will not work to motivate people to take risks and demonstrating that your conclusion did not follow from it.
You’re still not understanding the math here. If we’re looking at this from the military’s perspective, it’s also a win, because an identical quantity of bombs dropped come at the cost of 2 flight crews (and planes) rather than 3.
You had a mistake in your mathematical intuition. That’s OK, it happens to all of us here. The best thing is to admit it. (NB: it’s your argument that’s deeply flawed and not the conclusion, so raising other reasons why this would be a bad policy is irrelevant at the moment.)
I still can’t figure this out. Faced with the choice between leaving, having learned nothing, and continuing to lose karma for every damn post I make, what does your model recommend?
Say you start out with 100 pilots. You have two options:
Send all 100 pilots to Japan with full fuel tanks. 25 make it back alive.
Send 50 pilots to Japan with twice as many bombs. 0 make it back, but 50 are still alive.
No, the military just wants to accomplish its missions. If more pilots are alive after each mission, it means more pilots available for future missions.
Honest questions are far less likely to be voted down than wrong statements.
When the general case seems confusing, it’s often helpful to work out a specific example.
Let’s say that there are 40 targets that need to be bombed, and each plane can carry 10 bombs normally, or 20 bombs if it doesn’t carry fuel for the return trip. We’ll assume for simplicity that half of the bombs loaded on a plane will find their targets (accounting for misses, duds and planes shot down before they’re finished bombing).
Then, with the normal scheme, it would take eight flights on average to bomb the forty targets, and six of those planes would go down. If instead the planes were loaded with extra bombs instead of return fuel, it would take only four such flights (all of which would of course go down).
If there are eight flight crews to begin with, drawing straws for the doomed flights gives you a 50% chance of surviving, whereas the normal procedure leaves you only a 25% chance. If those are all the missions, it’s clearly rational to prefer the lottery system to the normal one. (If instead the missions are going to continue indefinitely, of course, you’re doomed with probability 1 either way.) And of course the military brass would be happy to achieve a given objective with only 2⁄3 the usual losses.
The difficulty with thinking in terms of “half-lives of danger” is that it’s the reciprocal of your probability of survival, so if you try and treat them as simple disutilities, you’ll run into problems. (For instance, if you’re facing a coinflip between dangerous activities A and B, where A consists of one half-life of danger and B consists of five half-lives, your current predicament is not equivalent to the “average value” of three half-lives of danger.)
What if there’s a hidden variable? Say, a newly-trained flight crew has skill of 1, 2, or 3 with equal probability. On any given mission, each bomb has a 10% chance, multiplied by the crew’s skill, to hit it’s target, and then at mission’s end, assuming adequate fuel, the crew has the same chance of returning alive. If they do so, skill increases by one, to a maximum of seven.
Furthermore, let’s say the military has a very long but finite list of targets to bomb, and is mainly concerned with doing so cost-effectively. Building a new plane and training the crew for it costs 10 resources, and then sending them out on a mission costs resources equal to the number of previous missions that specific crew has been sent on, due to medical care, pensions (even if the crew dies, there are certain obligations to any surviving relatives), mechanical repairs and maintenance, etc.
What would the optimal strategy be then?
Further complications aren’t relevant to the main point. Do you understand the theory of the basic example now, or do you not?
Yes, I understand the theory.
OK then. You can of course add additional factors to the basic model, and some of these will mitigate or even overwhelm the original effect. No problem with that. However, your original mathematical intuition about the basic model was mistaken, and that’s what I was talking to you about.
In general: let’s say someone proposes a simple mathematical model X for phenomenon Y, and the model gives you conclusion Z.
It’s always a complicated matter whether X is really a good enough model of Y in the relevant way, and so there’s a lot of leeway granted on whether Z should actually be drawn from Y.
However, it’s a simple mathematical fact whether Z should be drawn from X or not, and so a reply that gets the workings of X wrong is going to receive vigorous criticism.
That’s all I have to say about that. We cool?
It is a longstanding policy of mine to avoid bearing malice toward anyone as a result of strictly theoretical matters. In short, yes, we cool.