Owen
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Owen has not written any posts yet.
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... (read more)
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... (read more)
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:
Upvoted; thanks for providing the name "Dunning-Kruger" and the Oresme example!
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... (read more)