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One problem with this that I am already noticing is that I will feel less let down with myself if I admit that I have assigned a probability of (which I have) .25 to actually meeting my goal. I hope this will not be a significant detracting factor.
In my experience, this is a very legitimate concern. What you might want to do instead is set sub-goals: reach 200 posts by Saturday, 230 by the Saturday after that, etc. That way, you're giving yourself the chance to see now whether 4 posts per day is too much to expect yourself to handle, while at the same time making progress toward your big goal. And if you do find that that rate is too high, you can give yourself a chance to adjust your goal without just excusing yourself in advance for failing to achieve it.
I also suggest looking for high-rated posts about 10%, 20%, 30% etc. of the way from here to the end of the list, and writing their titles down as milestones. That way, when you reach those posts you'll get a nice reminder that you're making progress.
I feel like question 1 could be tweaked so that it's harder to put in wrong answers (in this case, not weakly increasing probability estimates). Maybe you could ask for the probabilities that humanity will go extinct in certain ranges of time (e.g. "How likely do you think it is that humanity survives to the year 2100 but goes extinct by 2200?"). Or, to circumvent the condition that the probabilities add to less than 100%, you could condition: "Assuming that humanity survives to the year 2100, how likely do you think it is that humanity then goes extinct by 2200?"
I only make these suggestions because I can imagine someone reading the original questions and thinking "Hmm, yes, it seems pretty likely that we annihilate ourselves by 2100: 40-60%" and then putting down 0-20% for part (e) because it's so much harder to think of ways to go extinct that take thousands of years.
And I would reverse the order of 6 and 7: "What is your level of education? If you are a college student, what is your area of study?" And if you want people's past experience to count too, you could ask instead "If you have or are earning a college degree, what is/was your area of study?"
When you use the actual numbers of people, you get those numbers by using the base rate: 10,000 women total, of which 100 have cancer (that's the base rate in action), of which 80 test positive, etc. So if you use the numbers 80 (= 0.8 0.01 10000) and 950 = (0.096 0.99 10000), you're not ignoring the base rate. You would be ignoring the base rate if you used the numbers 8000 and 960 (80% and 9.6% of the population of 10,000, respectively), but those numbers don't refer to any relevant groups of people.
You're forgetting the "base rate" in your calculation: the actual rate of cancer in the population. What you should really be taking the ratio of is (the fraction of all women that have cancer and test positive) / (the fraction of all women that test positive, whether or not they have cancer). In percentages, that's
(80% of the 1% of women who have cancer, who correctly test positive) = 0.8 * 0.01.
divided by
(80% of the 1% of women who have cancer, who correctly test positive) together with (9.6% of the 99% of women who don't have cancer, who test positive anyway) = 0.8 0.01 + 0.096 0.99.
So the ratio is (0.8 0.01) / (0.8 0.01 + 0.096 * 0.99), and that does equal 0.078.
I meant the first one: faster than light in both directions.
You can think of it this way: if any reference frame perceived travel from B to A slower than light, then so would every reference frame. The only way for two observers to disagree about whether the object is at A or B first, is for both to observe the motion as being faster than light.
Shinoteki is right - moving slower than light is timelike, while moving faster than light is spacelike. No relativistic change of reference frame will interchange those.
You are correct: moving from A to B faster than the speed of light in one reference frame is equivalent to moving from B to A faster than the speed of light in another reference frame, according to special relativity.
I think the error lies in this sentence:
"Presumably your chances of success this time are not affected by the next one being a failure."
I assume you think this is true because there's no causal relationship where the next shuttle launch can affect this one, but their successes can still be correlated, which your probability estimate isn't taking into account.
If you want to update meaningfully, you need to have an alternative hypothesis in mind. (Remember, evidence can only favor one hypothesis over another (if anything); evidence is never "for" or "against" any one theory at a time.) Perhaps the engineers believe that there is a 4% chance that any given shuttle launch will fail (H1), but you estimate a 25% chance that they're wrong and the shuttles are actually foolproof (H2). Then you estimate the probability that the first shuttle launch will fail (F) as
P(F) = P(F|H1) P(H1) + P(F|H2) P(H2) = (4%)(75%) + (0%)(25%) = 3%.
But the shuttle launch goes off ok, so now you update your opinion of the two hypotheses with Bayes' rule:
P(H1|~F) = P(~F|H1) P(H1) / P(~F) = (100% - 4%) (75%) / (100% - 3%) ≈ 74.2%.
Then your estimate that the next shuttle will fail (F') becomes:
P(F' | ~F) = P(F' | H1, ~F) P(H1 | ~F) + P(F' | H2, ~F) P(H2 | ~F)
= (4%) (74.2%) + (0%) (100% - 74.2%) ≈ 2.97%.
So the one successful shuttle launch does, in this case, lower your expectation of a failure next time. As the shuttles keep succeeding, you become gradually more and more sure that the shuttles are foolproof and the engineers are wrong. But if the launch ever does fail, you will instantly believe the engineers and assign no credence to the claim that the shuttles never fail. (Try the math to see how that works.)
Here's a practical suggestion: bake crackers. Buying gluten-free crackers can get annoyingly expensive, but it's not hard to bake your own, and they come with the following benefits:
- They're easy to bake in large amounts if you stock up on gluten-free flours like almond meal or rice flour (which will also save money in the long run)
- They won't go bad if you don't eat them within a day or two, so you don't have to worry about packing the right amount every day.
- Similarly, they won't go bad in the mail, so your parents might be able to do the baking for you if you're pressed for time.
- They're pretty close to the comfort foods I'm sure you're missing.
Easy recipe: Preheat oven to 350.
Mix together about 2 cups of different gluten-free flours.
Add some savory stuff like parsley flakes or sesame seeds if you want.
Add a tablespoon of oil and a couple tablespoons of water, and mix together.
(Add more water and oil if you can't get it all wet - some flours are drier than others.)
Roll the mixture out flat between two layers of parchment paper.
Remove the top layer of paper and score the dough into cracker shapes (I do a simple grid with the blunt side of a butter knife).
Bake on a cookie sheet in the oven for ~10 minutes. (You're looking for them to turn golden-y.)
Hope that helps!
Upvoted; thanks for providing the name "Dunning-Kruger" and the Oresme example!
You're right; maybe I'm overestimating my ability to explain things so that laypeople will understand. But there are some concessions you can make to get the idea across without the full background of complex linear algebra - often I use polarizers as an example, because most people have some experience with them (from sunglasses or 3D movies), and from there it's only a hop, skip, and a jump to entangled photons.
I do try to explain so that people feel like the explanation is totally natural, but then I often run into the problem of people trying to reason about quantum mechanics "in English", so to speak, instead of going to the underlying math to learn more. Any suggestions?
I can intentionally do lots of things, some of which cause entanglement and "collapse", and some of which don't. I'd say to them that it still seems like the conscious intent isn't what's important.
If you'd like to substitute a better picture for the layperson, I'd go with "disturbing the system causes collapse". (Where "disturb" is really just a nontechnical way of saying "entangle with the environment.") Then it's clear that conscious observation (which involves disturbing the system somehow to get your measurement) will cause (apparent) collapse, but doesn't do so in a special depends-on-consciousness way. And if they want a precise definition of "disturb", you can get into the not-too-difficult math of superposition and entanglement.
Perhaps that extremely simple systems, that no one would consider conscious, can also "cause collapse"? It doesn't take much: just entangle the superposed state with another particle - then when you measure, canceling can't occur and you perceive a randomly collapsed wavefunction. The important thing is the entangling, not the fact that you're conscious: measuring a superposed state (i.e. entangling your mind with it) will do the trick, but it's entirely unnecessary.
I used to believe the consciousness-causes-collapse idea, and it was quite a relief when I realized it doesn't work like that.
Upvoted because I like to see this kind of brainstorming, although I feel like the "strongly care about" criterion is a bit ad hoc and maybe unnecessary. To me it sounds more correct to say that Mr. IHJ doesn't care about his future selves, not that he doesn't have any.
Upvoted for noticing your confusion. At least two possible reasons come to mind:
Explanation 1: Luke has made many solid contributions in the past, and such contributors' comments tend to receive more upvotes than others' do, just by a kind of halo effect: "Luke's other posts are good, so he's a good rationalist, so this comment of his must be good too." I don't know how true this is: I've heard the idea suggested by other people here, but I've also seen several examples of top contributors receiving well-deserved downvotes in some cases.
Explanation 2: Luke's comment is genuinely more deserving of upvotes, since rysade's comment uses phrases like "I think" and "subtly changing", which downplay commitment and measurability, respectively, while Luke's comment indicates an explicit change he has already made. Again, I can't really speak for the people who upvoted Luke's comment (not even being one of them myself), but it seems plausible that this is at least one force at work in the disparity.
I don't know how much of each of these two hypotheses is truly at work here, or if there's something else going on that I've missed. (It's easy to come up with what are in my opinion less likely scenarios: Luke has made several phantom accounts to upvote his own comments and/or downvote others' similar comments, or someone else holds a grudge against rysade, etc.)
I'm about 15% through the lessons on Gregg shorthand here: http://gregg.angelfishy.net/ (This is my first comment, so I'm not sure how to do links. If someone would to point me to instructions, I'd be grateful.)
Mostly this comes under the "productive entertainment" heading, like knitting, but there's the possibility that knowing shorthand will come in useful in the future, e.g. for taking more complete lecture notes or fitting more words on a postcard.
My goals for this project are to (1) work through all the units on the website, (2) improve my speed to at least my current longhand speed, and (3) write shorthand as fast as people talk.