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?"

Thanks. I'm pretty sure I understand now. Although I'm not sure why I get the correct answer when I'm working with the actual numbers and not percentages when I do the math wrong.

But when I do the math like you wrote, I get the right answer for the precentages. So I get that part. But aren't I ignoring the base rate in the actual numbers one? Or no?

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.

My question is whether he meant to say

• 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

or

• moving from A to B faster than the speed of light in one reference frame is equivalent to moving from B to A slower than the speed of light in another reference frame

both of which involve moving faster than light.

Second 'faster' should be 'slower', I think.

Forgive my ignorance, but... if distance is defined in terms of the time it takes light to traverse it, what's the difference between "moving from A to B faster than the speed of light" and "moving from B to A"?

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:

1. 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)
2. 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.
3. 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.
4. 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!

It seems to me that it is easier to get people to realize just that they can't use their regular language to understand what is going on than to actually explain it. People seem to have issues with understanding this primarily because of Dunning-Kruger and because of the large number of popularizations of difficult science that just uses vague analogies.

I'd ask "ok. This is going to take some math. Did you ever take linear algebra?" If yes, then I just explain things. When they answer no (vast majority of the time)I then say "ok do you remember how matrix multiplication works?" They will generally not or have only a vague memory. At that point I then tell them that I could spending a few hours or so developing the necessary tools but that they really don't have the background without a lot of work. This generally results in annoyance and blustering on their part. At this point one tells them the story of Oresme and how he came up with the idea of gravity in the 1300s but since he didn't have a mathematical framework it was absolutely useless. This gets the point across sometimes.

Edit: Your idea of using polarization as an example is an interesting one and I may try that in the future.

And if they want a precise definition of "disturb", you can get into the not-too-difficult math of superposition and entanglement.

I'm a math grad student and I consider the math of entanglement and the like to be not easy. There are two types of consciousness-causes-collapse proponents. The first type who doesn't know much physics will find entanglement to be pretty difficult (they need to already understand complex numbers and basic linear algebra to get the structure of what is going on). Even a genuinely curious individual will likely have trouble following that unless they are a mathematically inclined individual. The second, much smaller group of people, are people who already understand entanglement but still buy into consciousness-causes collapse.They seem to have developed very complicated and sometimes subtle notions of what it means for things to be conscious or to have intent (almost akin to theologians). So in either case this avenue of attack seems unlikely to be successful.

If one is more concerned with convincing bystanders (as is often more relevant on the internet. People might not change their minds often. But people reading might), then this could actually do a good job when encountering the first category by making it clear that one knows a lot more about the subject than they do. This seems to empirically work in real life also as one can see in various discussions. See for example the cases Deepak Chopra has try to invoke a connection between QM and consciousness and he gets shot down pretty bluntly when there's anyone with a bit of math or physics background.