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orthonormal comments on Bayesians vs. Barbarians - Less Wrong
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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.
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?
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.
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)?
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.
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.
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...
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.