Breaking News: There is Sexism on Twitter

(cross posted on the GALS blog)

“Gross”, “disgusting”, “nasty”. “Get away from me”.

What could the internet have found so revolting? You’d think the subject matter of the twitterati’s latest target was a new sex tape that involved both necrophilia and bestiality and was thus finally shocking enough to horrify the mainstream judgement cloud that is Twitter (until the next trending topic came up, of course). Or perhaps it was an Actual Bad Thing like a celebrity domestic abuser.

Ah, me, no. The grossest thing the internet could imagine was a woman somewhere out there in the world, not applying sharp metal blades or hot melted wax to her skin. The horror!

We, the reasonable majority, might start to think about the women that we know, how in particular, they are not one unshaven day away from causing us to vomit every time they walk into a room. We might start to think that a twitter storm implying such a thing might start to make women put down, self-conscious and shamed. We might come to believe that sentiments expressed with such internet behavior are foolish and harmful, and that we need to push back. And we would be right.

The Occasion: No Shave November. Also known as Movember, or Novembeard, NSN is a yearly tradition in which people don’t shave for a month, in an effort to raise awareness and money for prostate cancer research. As you may be able to tell from the latter naming options, it has traditionally been focused on men. I don’t really have a problem with that. I understand that cancer research and awareness can be best served by snazzy, hip campaigns that appeal to people’s self-interest and sense of identity. This tactic can go terribly wrong, of course, as we’ve seen in the ‘pinkification’ of breast cancer. But in general, it’s fine for Movember to involve mainly men and market the idea mainly to men and even to emphasize the manliness of beards in order to do it.

But. But! When a phenomenon like No Shave November goes viral, it becomes so decentralized as to lack any organization that could alter the event to be more inclusive. This has obvious benefits, since it’s supposed to be, in some ways, something that people (read: men) just do because it’s fun and silly and exciting and yes, also because it’s for a good cause. Unfortunately, this means that the public face of No Shave November, as analyzed through twitter, becomes a cesspool of male privilege and pangendered body shaming.

No shave November does not apply to females… I repeat: No shave November DOES NOT apply to females. That is all”
“Just Witnessed A Female Who C L E A R L Y Started -No Shave November-. Ughhhh. Nasty AF”
“No shave November doesn’t apply to women. That’s disgusting.
“No Shave November is meant for men, NOT women!!!”

And I could go on and on and on and on…(note: these came from all genders).

Seriously, now? Has women’s body hair been killing people? Engaging in public urination? Eating people’s hamsters without justifiable cause? No? Oh, it’s just existing on women’s bodies in a totally sanitary and natural way in the same way it does on men’s bodies. And that is apparently enough to provoke an onslaught of self-indulgent narcissistic personal preference sharing tweeting, all of it entirely oblivious to the vast social and political consequences of such an overwhelming condemnation of women who do not shave their bodies.

I, for one, am fed up. Fed up with the silliness of caring so much about what other people look like, even when it doesn’t affect you. Fed up with the totally unfair beauty standards to which women are held and shamed if they do not. Fed up with the internet helping to create a society where it’s ok to make a perfectly normal preteen girl feel like she’s less of a woman if she doesn’t pull out the razors immediately on her twelfth birthday. And really really fed up with a culture that focuses more on the fact that women aren’t shaving than on the fact that they’re fighting prostate cancer.

But what is to be done? The internet is a devastatingly unappealing place at times, but it would be politically lazy to therefore do nothing. We have the choice to let the internet conquer feminism, or to make feminism conquer the internet.

Sexists may be all over the internet for now, but remember: their public forums are ours as well. We can use the same tools and turn their awful messages on their heads. We can call out sexism where we see it. We can spread supportive, healthy messages to the entire Internet community.

And we already are! The feminist blogosphere exists, of course, but even just in this case, check out this woman, who is calling out sexism. And this guy was really happy we, the anti-sexists, existed. Sure I received some unpleasant replies to my requests for a saner, less misogynistic world, but again, if the sexists can use twitter as a public forum, so can we. We can say things like, “Stop shaming women for their personal choices. Especially if they’re trying to fight prostate cancer” We can even change some minds. We can hopefully reach many who may be made hopeful by the sheer existence of those willing to question the assumption that women must naturally have a higher standard of beauty inconvenience.

A woman who doesn’t shave her legs does not harbor the seeds of destruction of a civilized and hygienic society, and one who does it in the name of raising money for prostate cancer research is praiseworthy, not disgusting, and she should be lauded, not shamed. This is worth saying. Over and over again, in conversation and on the internet. It may be saddening or disturbing that it has to be said at all, but that is no excuse for inaction on our parts. If feminism has done anything, it has given us a voice. Let’s use it to make a more equal society, 140 characters at a time.

Also check out a friend’s take on the same issue at Teen Skepchick.
If you want to donate to the cause, check out the Prostate Cancer Foundation

Atheism: Questions and Answers

So SA got a bunch of emails from an English class in Chicago asking us about our religious beliefs. Apparently they’re doing some kind of project on religion, so Mike Mei and I I gave them our answers on the condition that I could post them. Here they are; I’d love to know what you think! (Note: Yes, there is some overlap, which I warned them about, and yes they are fairly short. Whatever.) If you have other questions you want us to ask about atheist (or in my case, Jewish atheist) identity, please ask in comments! Similarly if you disagree with any of my answers. 
(Partially cross-posted at the UCSecular Blog)

Question Set 1:

1. What made you want to follow the faith that you are following?
I am an atheist, and I identify as such because I desire powerfully to have an accurate and true understanding of the world around me and my best rational inquiry has led me to the belief that there is no god.

2. How has your religious belief affected you and those around you?
My atheism, perhaps surprisingly, affects my life relatively little. Most of the time, the notion of god happening not to exist is not on my mind. However, the secular community has become one of my communities of choice, and spending time with such people has enriched my life, the way that such communities do. Similarly, I feel that my atheism has not affected those around me, except that I perhaps engage in more friendly debates about religion than I otherwise would.

3. What is the main concepts/pathways your religion follows?
There is almost certainly no god, meaning is to be found by individual humans through choice and ethics are to be derived from science and human values.

4. How do you define the relationship between the sacred and its followers?
The sacred is a cluster of powerful human intuitions and emotions surrounding these intuitions; followers of the sacred are people who have decided to dedicate some portion of their physical or mental lives to considering and engaging with these intuitions, either individually or in groups with shared tenets or practices.

5. How do you know that you have accomplished your purpose on Earth? Why do you believe you were put on Earth?
I do not believe I was placed on Earth; I believe I was born. I have no external purpose, and the only guidepost I can use to decide whether I have achieved any purpose at all is my own reason and judgment.

6. Describe how you find meaning in your life?  What steps have you taken to achieve completion?
Meaningfulness is also a constructed social understanding of shared human intuition, and so I find it in many of the ways that most humans access those satisfying and powerful emotions: I learn about the things I find interesting, I spend time with people I admire and care about, I set goals for myself that I think are useful, ethical and challenging and try to achieve them and I try to think deeply about the world.

7. Describe how the followers of your religious belief find meaning in their life? What are the steps necessary?
Because atheists are not bound by a series of strict beliefs, tenets and laws, they all find meaning in their own ways. Some are existentialists, who find meaning through choice and experience, some are humanists, who find meaning through ethical practice and community building, some are nihilists, who do not believe in meaning, and some are something else altogether. There are no prescribed steps, nor prescribed meaning.

Question Set 2:

1.      What kind of religion do you believe in? ex. : Christian, Jewish, Buddhist
I am an atheist.

2.      How long have you been practicing this religion?
I have been an atheist since I was approximately 11 years old (8 years ago) but have been actively engaging with the atheist community for 3 years.

3.      Do you participate in daily or weekly meetings/worship services? If so, how often?
Yes, I go to weekly secular meetings at my school.

4.      Why are you drawn to this particular religious philosophy? Why do you choose it?
I desire powerfully to have an accurate and true understanding of the world around me and my best rational inquiry has led me to the belief that there is no god.

5.      In your personal experiences, what did this belief bring to you? How does it influence your life? Why this is important to you?
Atheism has been tremendously liberating and satisfying belief to hold. It makes me feel like a more rational person, a more consistent person, and a more thoughtful person. I can feel proud of this belief, knowing that it is supported by evidence and that it is commensurate with a worldview in which empiricism, science and critical thinking are privileged above dogmatism and tradition. It is a progressive approach to the world, and best of all, it is true.

6.      Can you list and briefly explain some specific events that happened in your life, which this specific religion was involved? (it helped you to make decisions, it told you how to deal with the relationship with people, etc.)
Because atheism is simply the lack of belief in a god, it has never helped me make a specific decision, but the belief that there is no afterlife has certainly made me have much more of a concern for human life now.

7.      How do you identify the word “God”? How do you describe your relationship with the god?
The word God refers to our cultural understanding of a being which satisfies intuitions and emotions we have about the need for objective truth, meaning and morality, the existence of vast and majestic power and the desirability of the existence of an eternal onlooker, judge, king and parental figure.

8.     (Optional) Do you have any friends or family members who are also believe in the same religion?
Yes. Both of my parents are atheists, as are many of my friends and community members.

To check out Mike Mei’s answers, click here, and to check out his blog, click here.

Surface Level Thinking Bores Me to Tears: NOMA, Evolution and the Philosophy of Religion

Michael Ruse, who recently came to speak at the University of Chicago, seems to have exactly the kind of deeply reasonable ideas which are entirely correct and yet useless precisely because they never engage with the more difficult aspects of the topic. Because these kinds of ideas are so obvious in theory, all of their flaws arise in application. That’s probably uncharitable. Knowing the atheist community as I do, it actually is a controversial notion that in order to be better, more convincing, not to mention more ethical arguers and persuaders for our truth claims about the universe, it helps to understand the other side. And when I say understand the other side, I mean take religion seriously, possibly as seriously as it takes itself. In human history, ideas tend not to last this long unless they are very compelling, either because they are true or because they have something else, and dubbing that something else ‘comfort’ or ‘usefulness’ and then completely ignoring it when you make arguments (either because you don’t acknowledge the need for comfortable/useful/something else ideas and thus fail to build back up pillars, or because you don’t take it into account when you’re discussing the very question of how religion has lasted so long) is really not acceptable. So I was gratified to hear Ruse say something very much along these lines, though I harbor little of the hatred of New Atheists that seems to burn bright in his chest. (Though he did say this, interestingly enough).

Nonetheless, because I am entirely convinced of this proposition and I think any intellectually honest and curious person should be, too, it strikes me as an argument without an insight, a talk without a catalystic novelty at its base, and this is disappointing. Especially since it soon became clear that Ruse falls prey to a common trap: in order to emphasize the similarities or compatibilities of two worldviews or philosophies, only criticize the most egregious wrongs of either side and claim that the middle is really anyone’s game. Please, people, do not do this. Do not claim that you are both a Baarthian and a Kierkegaardian but also a Humean, and therefore believe that resurrection-believers are nuts. Do not claim that so far, religion (qua religion) has donated nothing of use to science, but perhaps in the future, it very well might. Do not appeal to the strawman of ‘scientism’ and then grasp the remaining scraps of straw in the form of wronglyasked questions (why is there something rather than nothing?) or examples of where religion might be of some descriptive use. And, while this is a but off-topic, do not sweat arrogance and pomposity out of every pore by claiming to be a conservative Protestant atheist, and thus better than the religious by being an atheist and better than the atheists by claiming that if you were religious, you’d be better at it then them.

Ruse actually did have some really interesting things to say about metaphor and its use in science, but I’m going to leave that to another piece. I really want to focus on this question of the philosophical intersection between science and religion, how they conflict and why, and whether NOMA, which Ruse seems to generally favor, should be taken seriously.

No, I don’t, actually, because H. Allen Orr did it better. Read this: (hattip: Charles Huff). Now. Then come back.

Let me be absolutely clear: I love (almost) everything about this piece. This piece needs to be spread far and wide. I will begin to try to emulate this piece through my blogging. It is fantastic.

More specifically:
1. The exquisite self-awareness redolent in the acknowledgement of not only weak or shoddy but simply pathetically overused arguments is so refreshing I can’t even stand it. I have arrived at a point in my intellectual life where I find novelty and creativity in thinking so very much more important than being right by sheer virtue of never saying anything that borders on unreasonable, which is mostly a result of cowardice. Orr’s quip about the Natural Law of Scientists (by which he really means atheist internet arguers) Mentioning Crusades made me want to cheer.

2. The entire first paragraph is just…right. Exactly and fundamentally correct.

3. Of course I deeply appreciate Orr’s call against an oversimplification of religion, but what’s so funny is even to call it that would be an oversimplification. A charge of oversimplification only makes sense when it is brought against an argument which has made attempts to sincerely understand and categorize a topic or phenomenon, and has made some unfortunate and grievous mistakes by overlooking important analytic distinctions. But, that’s not even the issue here. Gould undertook a radically absurd redefinition of religion. To call it an oversimplification would be a compliment.

4. The bit about Gould’s nonsensical use of pseudo-Aristotelianism: LOVE. LOVE times a million. I mean, really. No only is that a bastardization of Aristotle, a philosopher who should really be taken more seriously insofar as he is revered but in my opinion not well-understood, but I also read David Deutsch’s book The Beginning of Infinity this summer, and he along with many others in the rationalist community are pretty sick of the idea of truth as an average. When two predictions come about as a result of two entirely different explanations of how the world or something else works, picking and choosing bits is really not the way to go. In fact, you’re just going to get shoddier data. How this relates to politics is a fascinating set of confusions I currently have bouncing around.

5. Orr’s incisive analysis of Gould’s conception of religion coming squarely out of a scientific tradition is not only right on, but is something I’m especially sympathetic to since I’m reading Abraham Joshua Heschel’s God in Search of Man, which is decidedly not materialistic in its philosophical approach. Really beautiful book, by the way.

6. I didn’t know that, as Orr says, “J.B. S. Haldane was an unabashed mystic” but it makes so much sense! Dawkins quotes his, “Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose.” all the time as an example of positive scientific awe and wonder, but it’s always struck me as pretty mystical and anti-scientific. It depends on how you interpret it, of course. The context is that the prior sentence is “I have no doubt that in reality the future will be vastly more surprising than anything I can imagine.” which may imply that the second sentence is simply a furthering of the thought that the future will be exciting and progress between now and then will be so wonderfully expansive that we simply cannot even conceive now of the questions that will be asked in the future, let alone the answers. But if the first sentence is a personal opinion which is drawn from the larger philosophy explicated in the second sentence which appears to posit fundamentally ineffable concepts, we have a problem.

7. The offhand description of different spheres as a probably “bastardized legacy of Kuhn’s” is right on and also hilarious.

Small points of disagreement:

1. “The point is that it is dishonest to pretend that the Crusades count against theism but that Stalin doesn’t count against atheism.” Possibly true, but possibly not. There’s a different between incidental truths and relevant truths, and which is which depends largely on the neurobiology of religion and what your philosophy of religion is. So…not quite as clear cut as he’s making it out to be. Maybe I should write to him!

2. I get seriously annoyed when people bring up ‘scientism’ as a thing, as I said above. It’s not a thing. Yes, there are logical/mathematical truths. Some people have made what I find to be compelling arguments that those are in fact themselves empirical. You can make all kinds of logical systems if you want; logical is not a single thing. All the other examples are or could be scientific (if they were done more rigorously). Certainly not everything is scientific, but everything is subject to reason. If you don’t believe that, that’s fine, but seriously, people, it’s not a weakness of the rational worldview. Ruse got this totally wrong.

That’s all for now; if you think I got something wrong, or right for that matter, please tell me!

The Dark Arts, or How to get more rational by taking online quizzes

Remember that quiz you all took? This one?

Let’s talk about it.

1. How long will this quiz take you?
I realize that it’s hard to estimate when you have no idea what the quiz is about, and I’m also aware that I may have skewed this by promising it would take under 10 minutes, but this question was meant to illustrate the planning fallacy. (A paper about it here and more information here). People tend to underestimate how much time something will take them, even if they have experience of going over time. This applies to a wide range of activities, from carpentry to origami, and does not apply to disinterested observers guessing about how long something will take someone else.

When we were discussing it at our club meeting, one of the club officers, Mike Mei, pointed out that this might also be an example of the Dunning-Kruger effect, in which unskilled (in a given area) people overrate their abilities in that area, essentially because they lack the knowledge to see where they have failed. There is a corrollary effect, in which skilled people underrate their abilities, because they spend time with people even more skilled than they are and have a better understanding of their own limitations.

The answers I got from SA were, in minutes: 10, 2, 10, 2, 5, 3, 2, 1 (possibly a 10), and blank. They all took between 3 and 7 minutes, so it’s possible the Dunning-Kruger effect was stronger than the planning fallacy here

(1.b.) On the original quiz, which I gave to the SA, the first question also had: How many questions do you expect to get right? which was meant to illustrate much the same points. I took this off since not all the questions have right and wrong answers.

2. Samantha was part of the Intervarsity Christian Fellowship in college and was abstinent until marriage. She has four children and does not use birth control. Is it more likely that she is a teacher, or a Christian and a teacher?

This is a spin on Jane being a feminist and a bank teller, which is a classic thought experiment/trick question in psychology. One example in a psychology presentation can be found here. It is a demonstration of the representativeness heuristic, in which people estimate probabilities of events by analyzing the data they have available to them, rather than by being aware of all the data they don’t have. In this case, people focus on the information I gave, which points strongly to Samantha being a Christian. This gives us a deviance from a Bayesian calculation, in some cases because we neglect the base rates of an event (this would be a prior), but in this case because of the conjugation fallacy. This fallacy occurs when we assume that a more restricted situation is more likely than a more general one. In particular, if we say that Samantha is more likely to be a Christian and a teacher, then we are claiming that the probability that Samantha is a Christian AND that Samantha is a teacher is less than the probability that Samantha is a teacher of any kind, which is clearly false. The wikipedia article has the math, but what you really need to see is this:

If A is the probability that Samantha is a teacher of any kind and B is the probability that Samantha is a Christian, we see that the overlap (C) can’t be larger than either A or B.

To my disappointment, SA answered with 2 saying teacher, 5 saying christian and teacher and two people rebelling against the two options I gave them to say:

“Just a Christian. Women must be oppressed and pregnant. Quote the Bible”
“The probabilities seem similar, though one should never take professed faith at face value.”

To be fair, these answers actually have a lot of merit. Even though it wasn’t the point of the question, it probably is much more likely that Samantha is a Christian than that she is either a teacher or both. Given that, it’s probably also true that the probabilities of her being a teacher and both being a teacher and a Christian are similar (if the probability of her being a Christian is high enough). Don’t believe me? Pick some probabilities at random and do the math! It’s just multiplication, I promise.

I find the last bit particularly intriguing. Perhaps this intrepid secularite is referring to the phenomenon of belief in belief?

By the way, if you were confused about all that Bayes talk, here’s a fairly simple explanation of Bayesian probability.

3. Do you think the percentage of countries in the UN that are African countries is higher or lower than 65%/10%? What is the percentage of countries in the UN that are African countries?

If you’ve already checked out both instantiations at the quiz, you probably realized this is one of the places they deviated. This is supposed to illustrate the anchoring effect, in which our analysis of what answer is reasonable is heavily affected by the information we’re given to start with. Sometimes this is because we adjust from that number, and sometimes because our brains remember information consistent with the number we start with. This can occur in context, as in this question or a starting bid for a salary, or out of context, as in spinning a Wheel of Fortune before answering the question (this link goes to a generally great paper). Crazy, isn’t it? But it’s true. It’s also worth pointing out that, despite the claim of some SA members that science people might be less prone to the fallacy than humanities people, even those who are reminded of the anchoring effect and told to avoid it are subject to it, at least when the anchor comes externally (as in this quiz). However, with internally created anchors (if I hadn’t given the first part of the question), warnings and high Need for Cognition do lower the extent of the effect.

SA Answers:
65%: 10%, 10%, 30%, 30%, 20% – Mean: 20%
10%: 18%, 52%, 8%, 13% – Mean: 22.75%

Oddly, the SA at UofC appears to be immune to the anchoring effect. Or something.

4. (5 seconds) Guess the value of the following arithmetical expression:  8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = ? OR 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 = ?

This is the same issue. People tend to look at the first few numbers, multiply, and then adjust, since they’re asked to do it in 5 seconds.

Answers from SA
Descending order:  400,000; 1,000; 1,024; 500  Average: 100,631 (obviously not particularly useful given the high variance). Without the outlier, the average is 841.33
Ascending order: 1,000; 900; 16,320 (calculated, not guessed); YAY MATH!; 4,000;   Average: 5555

Again, not entirely expected, but that’s ok.

Source: I got both of these questions straight from here:

5. 1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she has breast cancer?

6. 1500 out of every 10,000 men at age forty who participate in routine screening have prostate cancer. 1300 of these 1500 men will get positive screening tests. 8,000 of the men who do not have prostate cancer will also get positive screening tests. A man in this age group had a positive test in a routine screening. What is the probability that he has prostate cancer?

You probably noticed that these are the same question, one with percentages, one with numbers. Apologies for the typo in the second question, by the way; that’s been fixed. These questions ask for a Bayesian calculation of probability. As someone has pointed out in the comments, it might seem like the test is asking for mathematical proficiency rather than rational abilities. I take the criticism willingly, but nothing on this quiz requires more than basic multiplication. Knowing how to set up a Bayesian calculation may be mathematical in some sense, but I would argue that it’s also simply something a rational person should know how to do, in the same way that calculating iterated probabilities of coin flips requires multiplication but if you think that the probability of getting heads at least once when you flip a coin twice is .5 + .5 = 1, there’s a problem that goes beyond arithmetic. This will become even more clear when I demonstrate the answer to this problem.

The way this works is as follows. We know that some people have cancer and some don’t, and some people get positive tests and some don’t. So we set up a table. The answers will be put in as (breast cancer problem numbers, prostate cancer problem numbers).

Has Cancer
Doesn’t Have Cancer
Positive Test
Negative Test

So for prostate cancer, the numbers are all given

Has Cancer
Doesn’t Have Cancer
Positive Test
( , 1300)
(, 8000)
Negative Test
(, 200)
( , 500)

For breast cancer, we have to do some calculations. For ease’s sake, let’s pick 10,000 as our total number of people (though it doesn’t matter). So of 10,000 women, 1%, or 100, have breast cancer, so our left column must add up to 100. 80% of these women will get a positive test, so 80 of them will and 20 won’t. Now we’re considering 9900 women who don’t have breast cancer, 9.6% of whom (or about 950) will get a positive test anyway leaving 8950 for the final quadrant.

Has Cancer
Doesn’t Have Cancer
Positive Test
(80, 1300)
(950, 8000)
Negative Test
(20, 200)
(8950, 500)

So if you get a positive test, you know you’re in the top row. If you’re a women who got a positive mammography, you have an 80/(80+950) = 7.76% chance of having cancer, and if you’re a man who got a positive test for prostate cancer, you have a 1300/(1300+8000) = 12.9% chance of having cancer.

From SA, who only got the breast cancer problem: 8/9 = 88%, 9.8%, 70.4%, 9.5%, 90.4%, 10%, 90.4%

Not to engage in scare rationalism here, but this is a problem. This means that women who go and get positive mammographies might be overestimating their probability of having cancer, and therefore undergoing possibly unnecessary biopsies, tests, chemotherapy, radiation, hospital visits, with the fear, stress and bills that come along with them, by an order of magnitude. Not good, people, not good.

And look what just came out: NYTimes: Considering When It Might Be Best Not to Know About Cancer

7. There are four cards on a table. Every card has one side which is white or black and one side with a number on it. The Rule: Every card with a white side must have an even number on the other side. How many cards (and which ones) must you flip in order to check if all four cards follow this rule?

8. You are an employee at an all age party venue, and people are allowed to come in with drinks. You see a group of four guys coming in, all carrying red Solo cups. One has an ID which says he’s 19, one is drinking orange juice, one is drinking beer, one has an ID which says he’s 24. Assuming you are accurate in your assessment of the drinks and all the ID’s are real, whose IDs/drinks do you check in addition to the information you already have to make sure no one is drinking illegally? 

Congratulations to whomever realized that these are the same problem. In  both cases you have four instantiations of an element of the problem with two pieces of information associated with it, only one of which you currently know. (4 cards, each has a number and a color; 4 people, each has a drink and an age). You are given a rule: If x, then y. If white card, then even number on opposing side. If drinking alcohol, must be 21. Now, if-then statements with x and y can be written four ways.
1. If x, then y is the original statement.
2. If y, then x is the converse.
3. If not x, then not y is the inverse.
4. If not y, then not x, is the contrapositive.

What you’ll notice if you’ve taken logic is that 1 and 4 are equivalent, and 2 and 3 are equivalent. So we have a rule, so we have to check it and its equivalent form. In these cases, if white then even must be checked (so check the white card) and if alcohol then at least 21 must be checked (so check the guy with beer), and also the contrapositive: if odd (not even), then black (not white), so you check the ‘9’ card, and if 19 (not at least = less than 21), not alcohol, so you check the 19 year old. The other ones don’t matter! So what if the even number has a black face on the other side? That’s like saying that if you’re 21 and above you must drink alcohol!

If you totally didn’t follow this, check out this link.

The cool thing about this question, called the Wason Selection Task, is that people are universally pretty bad at the card example and pretty good at the people example. The explanation given is that people are better at thinking about people and cheating (people possibly breaking rules) than abstract logical concepts. Maybe you agree?

SA Answers: Check the ‘2’ card, check the beer & juice; Check the ‘2’ and white cards, check the 19 year old’s drink and beer drinker’s ID; Check all the cards, check all the people except the 24 year old; Check the black card, and the one drinking orange juice and the one drinking beer; Check the ‘2’ card, check all of the people; Check the ‘2’ card, check the one drinking orange juice and the one drinking beer; Check all the cards, check the one drinking orange juice and the one drinking beer; Check the ‘2’ card, the ‘9’ card and the white card; check everyone’s drink.

Caveat: I phrased the question differently to them, and many thought that part of your job was to get the under 18’s out as well as check drinking legality, so you can’t draw that much from this sample. I would like to like to point out, though, that with the original Wason selection test part, no one got it right. Interesting…

9. A fair coin is tossed repeatedly until a tail appears, ending the game. The pot starts at 1 dollar and is doubled every time a head appears. You win whatever is in the pot after the game ends. Thus you win 1 dollar if a tail appears on the first toss, 2 dollars if a head appears on the first toss and a tail on the second, 4 dollars if a head appears on the first two tosses and a tail on the third, 8 dollars if a head appears on the first three tosses and a tail on the fourth, etc. This game can be played as many times as you wish (with a fixed fee paid every time). How much would you pay to enter this game?

I won’t lie, this one’s pretty math-y. Basically, when you’re deciding whether to take a bet, you should calculate something called expected value, that is, what do you expect to win? If you have a 50% chance of winning $2 and a 50% chance of winning nothing, then your expected value is .5*2 +.5*0 = 1, so you should be willing to pay a dollar or less (probably less, since people are loss averse).

Same thing applies. You have a 50% chance of winning $1 (if it’s tails the first time), then 25% of winning $2 (if it’s tails then heads), 12.5% of 4$, etc. The thing is that when you add up .5*1 + .25*2 + .125*4 + … you get .5 +.5 +.5 + .5 into infinity, and that adds up to infinity, which means the expected value from this bet is…infinity. Obviously there aren’t infinity dollars, and loss aversion plays a role here, but seriously, you should be willing to pay a lot of money to play this game. Crazy, huh?

SA Answers: $1, $1, $0.50, $3, 5 euro, $0, $2, $10, $2.

10. A magazine you’re interested in has three/two subscription options: Which do you choose?

Last one, promise. This one’s pretty simple. It’s all here, really: the basic idea is, we see that print/online sells for the same price as just print, so we think it’s a better deal, so we’re way more likely to pick it than if that second option isn’t there to favorably compare the third one to. Think about it next time you go to a restaurant! Cool, huh?

In SA, of the group that got three questions, 1/5 chose the cheaper one and of the group that got two questions, 1/4 chose the cheaper one.

(Thanks to Mike Mei for pointing me to this question)

Thanks for sticking with me through all that. This was my first venture into quiz making. I welcome comments and criticisms in the comments. Please also tell me if you’d heard of the fallacies/biases before taking the test! If you’re interested in this stuff and want to try to become more rational, I recommend Less Wrong and this Wikipedia Page. There’s a whole amazing world out there!