The Great Post-Abortion Debate

This is not about what the title might suggest.

I'm talking about the 20 or so unfinished & unpublished posts still in "draft" stage on Lem's blog. They are invisible to most readers. Some of them are accidental -- a few errant keystrokes led to an unwanted brain child -- the one from Freeman Hunt for example is just a title (titular posts is my tag for that). Others appear quite well along in development -- those from Pastafarian and Michael Haz, and Trooper York for example. There's even one from Darcy. Some of these authors are no longer contributors to Lem's blog. What should become of them?  Of course it's Lems decision, but I wish they'd stop by here and say hello. I'd like to wish them all Happy New Year.

"The Simple Logical Puzzle That Shows How Illogical People Are"

"Wason tells you that if a card shows an even number on one face, then its opposite face is blue. Which cards must you turn over in order to test the truth of his proposition, without turning over any unnecessary cards? Click on your answer in the interactive video below:"


"If you got it wrong, keep your spirits up: More than 90 percent of Wason’s subjects erred, too, and in quite a systematic way; the mistakes they made followed a pattern. “I feel very unhappy about my original choice,” a subject once told Wason, “but yes, I would still choose the same ones if I had to do the task again.” In that 1968 paper, titled “Reasoning about a Rule,” he wrote that these were “disquieting” results. The reigning assumption was that humans naturally reasoned analytically, but here was Wason’s subject admitting that, if given the choice, he’d be irrational again. It made Wason wonder: Is it the logical structure of the rules that make the puzzle difficult, or are people tripped up merely by the words with which the puzzle is expressed?

Scientific American: The Winners of the 2014 Best Illusion of the Year Contest

The First Prize winner of the contest, an illusion by Christopher Blair, Gideon Caplovitz and Ryan Mruczek from University of Nevada Reno, took the classical Ebbinghaus illusion, where the perceived size of a central circle varies with the size of surrounding circles, and put it on steroids by making it into an ever-changing dynamic display. Blair rhymed his 5-minute presentation Dr. Seuss-style.



Second Prize went to Mark Vergeer, Stuart Anstis and Rob van Lier from the University of Leuven, UC San Diego and Radboud University Nijmegen, for showing that a single colored image can produce several different color perceptions depending on the position of black outlines over the image.



Third Prize went to Kimberley Orsten and James Pomerantz from Rice University. Their illusion consists of three images, of which two match and one is a mismatch. Viewers see one of the matching images as odd, and mistakenly perceive the other two as identical.

NPR: How To Marry The Right Girl, A Mathematical Solution

"Imagine that you are interviewing 20 people to be your secretary [or your spouse or your garage mechanic] with the rule that you must decide at the end of each interview whether or not to give that applicant the job." If you offer the job to somebody, game's up. You can't go on and meet the others. "If you haven't chosen anyone by the time you see the last candidate, you must offer the job to her," Alex writes (not assuming that all secretaries are female — he's just adapting the attitudes of the early '60s).

So remember: At the end of each interview, you either make an offer or you move on.

If you don't make an offer, no going back. Once you make an offer, the game stops.

According to Martin Gardner, who in 1960 described the formula (partly worked out earlier by others), the best way to proceed is to interview (or date) the first 36.8 percent of the candidates. Don't hire (or marry) any of them, but as soon as you meet a candidate who's better than the best of that first group — that's the one you choose! Yes, the Very Best Candidate might show up in that first 36.8 percent — in which case you'll be stuck with second best, but still, if you like favorable odds, this is the best way to go.

Why 36.8 percent? The answer involves a number mathematicians call "e" – which, reduced to a fraction 1/e = 0.368 or 36.8 percent. For the specific details, check here, or Alex's book, but apparently this formula has proved itself over and over in all kinds of controlled situations. While it doesn't guarantee happiness or satisfaction, it does give you a 36.8 percent chance — which, in a field of 11 possible wives — is a pretty good success rate.

Also see Freeman Hunt's "Frank Advice for a Male Relative on Finding a Mate" Good Luck... and don't call me Frank ;)

Probability Pundit: Processing the 2016 GOP Primaries

What is Quantum Mechanical Superposition?

“What do I love when I love my God?”

The last two interview questions posed to John D. Caputo, a professor of religion and humanities at Syracuse University. The interview was conducted via e-mail, by Gary Gutting, a professor of philosophy at the University of Notre Dame and published by the New York Times.

G.G.: "If Derrida doubts or denies that there’s someone who guarantees such things, isn’t it only honest to say that he is an agnostic or an atheist? For most people, God is precisely the one who guarantees that the things we most fear won’t happen. You’ve mentioned Derrida’s interest in Augustine. Wouldn’t Augustine — and virtually all the Christian tradition — denounce any suggestion that God’s promises might not be utterly reliable?"

J.C.: "Maybe it disturbs what “most people” think religion is — assuming they are thinking about it — but maybe a lot of these people wake up in the middle of the night feeling the same disturbance, disturbed by a more religionless religion going on in the religion meant to give them comfort. Even for people who are content with the contents of the traditions they inherit, deconstruction is a life-giving force, forcing them to reinvent what has been inherited and to give it a future. But religion for Derrida is not a way to link up with saving supernatural powers; it is a mode of being-in-the-world, of being faithful to the promise of the world."

"The comparison with Augustine is telling. Unlike Augustine, he does not think a thing has to last forever to be worthy of our unconditional love. Still, he says he has been asking himself all his life Augustine’s question, “What do I love when I love my God?” But where Augustine thinks that there is a supernaturally revealed answer to this question, Derrida does not. He describes himself as a man of prayer, but where Augustine thinks he knows to whom he is praying, Derrida does not. When I asked him this question once he responded, “If I knew that, I would know everything” — he would be omniscient, God!"

"This not-knowing does not defeat his religion or his prayer. It is constitutive of them, constituting a faith that cannot be kept safe from doubt, a hope that cannot be kept safe from despair. We live in the distance between these pairs."

G.G.: "But if deconstruction leads us to give up Augustine’s way of thinking about God and even his belief in revealed truth, shouldn’t we admit that it has seriously watered down the content of Christianity, reduced the distance between it and agnosticism or atheism? Faith that is not confident and hope that is not sure are not what the martyrs died for."

J.C.: "In this view, what martyrs die for is an underlying faith, which is why, by an accident of birth or a conversion, they could have been martyrs for the other side. Mother Teresa expressed some doubts about her beliefs, but not about an underlying faith in her work. Deconstruction is a plea to rethink what we mean by religion and to locate a more unnerving religion going on in our more comforting religion."

"Deconstruction is faith and hope. In what? In the promises that are harbored in inherited names like “justice” and “democracy” — or “God.” Human history is full of such names and they all have their martyrs. That is why the difference between Derrida and Augustine cannot be squashed into the distinction between “theism” and “atheism” or — deciding to call it a draw — “agnosticism.” It operates on a fundamentally different level. Deconstruction dares to think “religion” in a new way, in what Derrida calls a “new Enlightenment,” daring to rethink what the Enlightenment boxed off as “faith” and “reason.”"

"But deconstruction is not destruction. After all, the bottom line of deconstruction, “yes, come,” is pretty much the last line of the New Testament: “Amen. Come, Lord Jesus.”"

Guest Post: "Why Do We Need to Talk About Race?"

"From my email and appreciated. Now one might not agree with every word. One might find fault with certain statistics. One might, rightly in my opinion, point out that not mentioning God explicitly makes the idea of an "arc of justice" absurd. (In his defense, he is addressing a TED audience, probably not a crowd particularly receptive to God talk though I'd have appreciated it if he'd tried.) However, listening past any faults or disagreements, there's much that is important there."

Freeman Hunt

Scientific American: "Equations Are Art inside a Mathematician’s Brain"

"When mathematicians describe equations as beautiful, they are not lying. Brain scans show that their minds respond to beautiful equations in the same way other people respond to great paintings or masterful music. The finding could bring neuroscientists closer to understanding the neural basis of beauty, a concept that is surprisingly hard to define."

In the study, researchers led by Semir Zeki of University College London asked 16 mathematicians to rate 60 equations on a scale ranging from "ugly" to "beautiful." Two weeks later, the mathematicians viewed the same equations and rated them again while lying inside a functional magnetic resonance imaging (fMRI) scanner. The scientists found that the more beautiful an equation was to the mathematician, the more activity his or her brain showed in an area called the A1 field of the medial orbitofrontal cortex.

Skipping down to the last three paragraphs...

The study found, for example, that the beauty of equations is not entirely subjective. Most of the mathematicians agreed on which equations were beautiful and which were ugly, with Euler's identity, 1+eiπ=0, consistently rated the most attractive equation in the lot. "Here are these three fundamental numbers, e, pi and i," Adams says, "all defined independently and all critically important in their own way, and suddenly you have this relationship between them encompassed in this equation that has a grand total of seven symbols in it? It is dumbfounding."

On the bottom of the heap, mathematicians consistently rated Srinivasa Ramanujan's infinite series for 1/π most ugly.

"It doesn't sing," Adams says. "I look at it, and I don't learn anything new about pi. And those numbers, 26,390? 9801? As far as I am concerned, you could switch in other numbers, and I couldn't tell the difference."

Scientific American

"Math Explains Likely Long Shots, Miracles and Winning the Lottery [Excerpt]"

I'm only including the birthday problem here. For the seemingly long shot, like the lotteries, click here.

The birthday problem poses the following question: How many people must be in a room to make it more likely than not that two of them share the same birthday?

The answer is just 23. If there are 23 or more people in the room, then it's more likely than not that two will have the same birthday.

Now, if you haven't encountered the birthday problem before, this might strike you as surprising. Twenty-three might sound far too small a number. Perhaps you reasoned as follows: There's only a one-in-365 chance that any particular other person will have the same birthday as me. So there's a 364/365 chance that any particular person will have a different birthday from me. If there are n people in the room, with each of the other n − 1 having a probability of 364/365 of having a different birthday from me, then the probability that all n − 1 have a different birthday from me is 364/365 × 364/365 × 364/365 × 364/365 … × 364/365, with 364/365 multiplied together n − 1 times. If n is 23, this is 0.94.

Because that's the probability that none of them share my birthday, the probability that at least one of them has the same birthday as me is just 1 − 0.94. (This follows by reasoning that either someone has the same birthday as me or that no one has the same birthday as me, so the probabilities of these two events must add up to 1.) Now, 1 − 0.94 = 0.06. That's very small.

Yet this is the wrong calculation to consider because that probability—the probability that someone has the same birthday as you—is not what the question asked. It asked about the probability that any two people in the same room have the same birthday as each other. This includes the probability that one of the others has the same birthday as you, which is what I calculated above, but it also includes the probability that two or more of the other people share the same birthday, different from yours.

This is where the combinations kick in. Whereas there are only n − 1 people who might share the same birthday as you, there are a total of n × (n − 1)/2 pairs of people in the room. This number of pairs grows rapidly as n gets larger. When n equals 23, it's 253, which is more than 10 times as large as n − 1 = 22. That is, if there are 23 people in the room, there are 253 possible pairs of people but only 22 pairs that include you.

So let's look at the probability that none of the 23 people in the room share the same birthday. For two people, the probability that the second person doesn't have the same birthday as the first is 364/365. Then the probability that those two are different and that a third doesn't share the same birthday as either of them is 364/365 × 363/365. Likewise, the probability that those three have different birthdays and that the fourth does not share the same birthday as any of those first three is 364/365 × 363/365 × 362/365. Continuing like this, the probability that none of the 23 people share the same birthday is 364/365 × 363/365 × 362/365 × 361/365 … × 343/365.

This equals 0.49. Because the probability that none of the 23 people share the same birthday is 0.49, the probability that some of them share the same birthday is just 1 − 0.49, or 0.51, which is greater than half.

Scientific American via Instapundit 

Manhattan Lullaby

On City Streets is an anthology of poetry. It was taught to me in high school in the mid-seventies. My sister and I liked it very much, and we read it together frequently. Here is a poem that I think especially captures the cozy feel the city can elicit. Incidentally, I thought of this poem when DBQ's and Freeman's new grand-son and son were born.

Manhattan Lullaby

(for Richard, one day old)

Now lighted windows climb the dark,
The streets are dim with snow,
Like tireless beetles, amber-eyed,
The creeping taxis go.
Cars roar through the caverns made of steel,
Shrill sounds the siren horn,
And people dance and die and wed-
And boys like you are born.

-Rachel Field

"Let Me Make This Perfectly Clear...

...If you like your healthcare plan you can keep your healthcare plan."

This was some chirbit advice given to Freeman Hunt a few months ago in response to something she wrote here or at Althouse. I think the message is more widely applicable.

[click on the green play arrow at the link]

Why the name change?

The name changed but the concept remains the same.
We want to have a place for commenting.
In an email exchange with Freeman, she said "Thank you so much for creating a new comment home!"
I thought, that's exactly what the place should be called. and my Picard said ... Make it so!

Again. As I said before. Its up to us to keep it. I'm doing my best to keep it alive. Fresh. People that disrespect what we are trying to do, will be asked to leave. I just decided.

People Get Ready

Nearly all of the old avatars are here. Hooray for that. And hooray for Lem!

Lem's made the place, but it's an awful lot of work to fill the space, so you'll now be seeing posts from time to time by guest bloggers. Hope you enjoy it.

-- Freeman Hunt

Rod Stewart - People Get Ready

I Got Fronted and it Feels Like A Hug

I checked in at the Big House Blog and There I was one more time. 'Fronted' because yesterday, one of us misinterpreted an Althouse vlog reference of the movie quote from Network (1976) - "I'm as Mad As Hell and I'm Not Going To Take it Anymore". The commenter thought that Althouse was saying she, herself, was mad at her commenters. When the reference was really about something else entirely.

I'm commenting up front to say I don't believe Althouse is Mad at her Commenters. You guys and I are her commenters, btw, that's how we started. I posted a Who Am I post and it barely broke 20 comments. Message received, not so loud but clear enough, I'm under no illusions.

Commenter Freeman Hunt asks a question in the James Bond Open Thread that feels somehow appropriate here, in some tangential lighthearted context that I know Althouse could stich together with the appropriate strings that get Betamax all excited.

"Is the Internet not the best venue for unemotional people to give hugs? I submit that it is."

And then she follows up...

"Or maybe my thinking is that immediate internal states are something you have but external states, immediate or otherwise, are something you choose."

And more...

"Emotions are wonderful."

"And no, I'm not talking about oneself versus the environment. I'm talking about how you feel inside versus what you express outside. Internally, people have immediate reactions to things. That's tough to choose at the moment of an event, but the pattern can be affected over time. Long term internal states are mostly chosen, I think. External states, apart from true reflexes, can be almost entirely chosen, in my opinion. (Then those go to affecting the pattern of internal states and so on.)"

After someone says she might be stoic, Freeman Responds...

"But I'm no pantheist. And I don't think that all emotions, even negative emotions, are bad.

But do I believe in the stiff upper lip? Sure."