Category Archives: Science

What Should Sleeping Beauty Say, Logically Speaking?

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Imagine that Sleeping Beauty agrees to take part in an experiment. First, she’s going to be given a special memory-loss drug that will make her forget what day it is. Then she’ll go to sleep. While she’s asleep, the people running the experiment will flip a coin. If the coin comes up heads, they’ll wake her up on Monday and ask her a question. If it comes up tails, they’ll wake her up on Monday, ask her the same question, give her the drug, let her fall asleep again, and then wake her up on Tuesday, asking the same question as before.

Because of the drug, however, she won’t know what day it is when she wakes up. Furthermore, she won’t know whether this is the first or second time she’s woken up. Each day will be a brand new experience for her. But each time Sleeping Beauty wakes up during the experiment, she’s told about the coin flip and the rule that says heads will mean she will wake up on Monday, and tails will mean she will wake up Monday and Tuesday. 

Now here’s the problem: Each time Sleeping Beauty wakes up and is told the rules of the experiment, she’s asked this question: “What are the odds that the coin flip came up heads?” That is, what are the odds that the coin came up heads and this is Monday (as opposed to tails and this is either Monday or Tuesday)? What should Sleeping Beauty say?

I came across this problem at the Quanta Magazine site yesterday. You may be surprised to learn that experts have been arguing about its solution for years:

The famous Sleeping Beauty problem has polarized communities of mathematicians — probability theorists, decision theorists and philosophers — for over 15 years…. This simple mathematical problem has generated an unusually heated debate. The entrenched arguments between those who answer “one-half” (the camp called “halfers”) and those who say “one-third” (the “thirders”) put political debates to shame… Halfers and thirders tend to remain firmly rooted in their view of the Sleeping Beauty problem. Both camps can certainly do the math, so what makes them butt heads in vain? Is the problem underspecified? Is it ambiguous?

So, should Sleeping Beauty say there is a 1/2 chance that the coin came up heads, since there’s always a 1/2 chance that coin flips come up heads and a 1/2 chance that they come up tails? Should Sleeping Beauty be a halfer?

Or should she be a thirder and say there is only a 1/3 chance it was heads? After all, if it’s Monday, she was awakened because the coin came up heads or tails. If it’s Tuesday, she’s awake because the coin came up tails. That means it’s twice as likely she’s awake because the coin came up tails. There’s a 2/3 chance the coin came up tails and a 1/3 chance it came up heads. It sounds like Sleeping Beauty should be a thirder.

But not so fast! There was only that one coin flip on Sunday and we all know that coins have a 1/2 chance of coming up heads! Maybe she should be a halfer?

The Quanta article is fairly long and delves into why halfers and thirders give the answers they do, as well as why they often resist changing their minds. The comments that follow the article are even longer and include mathematical formulas. I didn’t read all the comments, and I’ve never studied probability, but I left my own comment anyway:

I wasn’t a halfer or a thirder before reading the article. Now I’m a committed thirder.

If you were to simply ask Sleeping Beauty whether a fair coin toss came up heads, she should say the odds were 1/2. Without any other information, that’s the rational answer. But you’re asking what odds Sleeping Beauty should assign, given the additional information she’s been given about the experiment. Since today could be either Monday or Tuesday (as far as she knows), it’s more likely that the coin came up tails. The fully-informed, rational answer she should give is 1/3.

So I think Sleeping Beauty should say this each morning: “Given how coin flips work, the odds are 1/2 that heads came up. But given how coin flips work and given what you’ve told me about this peculiar experiment, the odds are only 1/3 that heads came up. I can easily flip back and forth between the halfer and thirder positions, but why should I ignore the additional information you’ve given me? Taking into account what I  know about the experiment, I must conclude that the odds are 1/3 that heads came up. If that makes me a thirder, so be it. Now where’s my prince?”

But she shouldn’t take my word for it. She should make up her own mind.

The author of the article, Pradeep Mutalik, responded to my comment and everyone else’s last night. I’ll post his response tomorrow in case you haven’t already rushed to the Quanta site to read it.

Meaning Is a Many-Splendored Thing, Part 2

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Roy Scranton’s “We’re Doomed. Now What?” begins with a different premise than Charlie Hueneman’s “Everything Is Meaningless – But That’s Okay” (which I went on about two weeks ago). Scranton thinks that global warming, escalating violence or a combination of the two will one day put our species out of its misery:

Today, as every hour brings new alarms of war and climate disaster, we might wish we could take Nietzsche’s place. He had to cope only with the death of God, after all, while we must come to terms with the death of our world….

We stand today on a precipice of annihilation that Nietzsche could not have even imagined. There is little reason to hope that we’ll be able to slow down global warming before we pass a tipping point….The West Antarctic ice sheet is collapsing, Greenland is melting, permafrost across the world is liquefying, and methane has been detected leaking from sea floors and Siberian craters: it’s probably already too late to stop these feedbacks, which means it’s probably already too late to stop apocalyptic planetary warming. Meanwhile the world slides into hate-filled, bloody havoc, like the last act of a particularly ugly Shakespearean tragedy.

It’s fair to say that without a major technological breakthrough on one hand or the collapse of the carbon-based global economy on the other, the amount of carbon dioxide in the atmosphere will continue to increase. That could have horrific consequences. A “runaway” greenhouse effect may have given Venus its thick atmosphere of carbon dioxide and average surface temperature of 842 degrees.

Scranton implies that we’re doomed because four common responses to the global warming crisis are seriously misguided. He says “denialists” deny the problem exists, “accelerationists” think more technology is the answer, “incrementalists” favor the kind of modest changes already being made, and “activists” argue that “we have to fight, even though we’re sure to lose”. He thinks “we respond according to our prejudices”.

He then calls attention to what could be thought of as a fifth type of response, except that it’s closer to no response at all. Scranton thinks nihilism “defines our current moment”. Too many of us believe that “if all is already lost, nothing matters anyway”. What he apparently has in mind is the point of view sometimes referred to as “existential nihilism”. That’s the idea that life, whether individual lives or human life as a whole, lacks meaning, purpose or value.

What evidence is there for this increasing nihilism? Scranton mentions four television programs (I’ve watched two of them – they’re very good). Maybe more convincingly, he says “you can see it in the rush to war, sectarianism and racial hatred”. There is also the advance of “scientific materialism”, which has been undermining religious beliefs since at least the 17th century.

But war, sectarianism and racial hatred aren’t examples of nihilism. Nobody goes to war because they think everything is meaningless. People don’t divide into sects because they lack purpose. Racists value some people more than others for no good reason. That’s stupid, but not nihilistic. Science conflicts with some religious doctrine, but people who take science seriously aren’t generally amoral. So, putting aside the issue of nihilism for the moment, what does Scranton say we should do?

Oddly, by the end of the article, Scranton has declared himself to be a kind of “activist”. He believes some of us will survive global warming. Our species isn’t due for extinction. Therefore:

…it’s up to us … to secure the future of the human species. We can’t do it by clinging to the progressivist, profit-seeking, technology-can-fix-it ideology of fossil-fueled capitalism. We can’t do it by trying to control the future. We need to learn to let our current civilization die, to accept our mortality and practice humility. We need to work together to transform a global order of meaning focused on accumulation into a new order of meaning that knows the value of limits, transience and restraint.

In other words, we need to find meaning in taking care of the planet, not in the all the stuff we can get from burning carbon. We can’t wait for the global carbon-based economy to collapse. If we want to keep the planet habitable for human beings (a few of us anyway) and other living things, we need to immediately cut back our use of fossil fuels.

I’m sure Scranton would like to explain how we can accomplish this. How will it come to pass that so many people will change their way of looking at the world, of valuing what oil and coal do for us? Global warming isn’t such an obviously imminent crisis that the powerful or the mass of humanity will quickly reorient their thinking. It’s not as if a planet-destroying asteroid is heading our way. Nor are we in danger of running out of fossil fuels in the foreseeable future. There are billions of tons of the stuff just waiting to be extracted.

But all that Scranton offers as a way forward is to cite Nietzsche. The German philosopher set forth a position known as “perspectivism”. It’s not exactly clear what he meant by that (clarity wasn’t one of his strengths), but the general idea is that we each have our own perspective on the world; none of our perspectives give us access to the world as it really is; so the best we can do is view the world from as many points of view as possible. Adopting more and more perspectives can get us closer to the truth, even though we can never attain absolute, completely objective, non-perspectival truth about anything at all.

At least that’s how Scranton interprets Nietzsche. Life may be meaningless. The planet is probably doomed. But human beings have a tremendous capacity to find meaning in all kinds of situations. We need to use that capacity to view the planet’s future from as many perspectives as possible, human and non-human:

We need to learn to see not just with Western eyes but with Islamic eyes and Inuit eyes, not just with human eyes but with golden-cheeked warbler eyes, coho salmon eyes and polar bear eyes…

If we can manage that, difficult as it may be, we may be able to stop the Earth from becoming another Venus.

Perhaps you agree about adopting new perspectives, but I think it’s highly unlikely that the world’s leaders or the mass of humanity will ever stop finding most of life’s meaning in the here and now, based on their own particular points of view. Denialists will continue denying there’s a problem. Technologists will continue looking for technological solutions. Incrementalists will advocate or settle for incremental change. Activists like Scranton will propose new ways of finding meaning, while nihilists won’t think it matters what happens.

My own view is that the human race may get lucky but probably won’t. We should, however, still make intense efforts to stop burning so much carbon, while making life as decent as possible for those of us who are already here, including the fish of the sea, the fowl of the air, and everything that travels or grows upon the earth (except maybe mosquitoes and poison ivy). We have to balance the near future in which life is hard for so many and the more distant future in which life may not be possible at all. We will probably fail, but it’s the right thing to do.

Who Knew the Pope Would Turn Out To Be a Christian?

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And a Christian who believes in science!

Pope Francis is upsetting a lot of people, including the fools and knaves seeking the Republican nomination (you know, the make-believe Christians who won’t admit nine people were murdered by a racist in Charleston because that would imply racism is still a problem in America).

The Pope issued a message to the world this week. From The Guardian:

Pope Francis’s encyclical on climate change, Laudato Si’, is the most astonishing and perhaps the most ambitious papal document of the past 100 years, since it is addressed not just to Catholics, or Christians, but to everyone on earth….

We need nature, he says, and we need each other….The care of nature and the care of the poor are aspects of the same ethical commandment, and if we neglect either one we cannot find peace….

Starting from that premise, he launches a ferocious attack on what he sees as the false and treacherous appetites of capitalism and on the consumerist view of human nature. For Francis, there is a vital distinction between human needs, which are limited but non-negotiable, and appetites, which are potentially unlimited, and which can always be traded for other satisfactions without ever quite giving us what we most deeply want. The poor, he says, have their needs denied, while the rich have their appetites indulged. The environmental crisis links these two aspects of the problem.

… The document is absolutely unequivocal in backing the overwhelming scientific consensus that anthropogenic global warming is a clear and present danger. It blasts the use of fossil fuels and demands that these be phased out in favour of renewable energy. But it is also explicitly opposed to the idea that we can rely on purely technological solutions to ecological problems….There will never be a technological fix for the problem of unrestrained appetite, the pope claims, because this is a moral problem, which demands a moral solution, a turn towards sobriety and self-restraint and away from the intoxications of consumerism.

The New York Times offers this summary (followed by selected paragraphs from the encyclical with explanatory comments):

Pope Francis has written the first papal encyclical focused solely on the environment, attempting to reframe care of the earth as a moral and spiritual concern, and not just a matter of politics, science and economics. In the document, “Laudato Si: On Care for Our Common Home,” he argues that the environment is in crisis … He emphasizes that the poor are most affected by damage from what he describes as economic systems that favor the wealthy, and political systems that lack the courage to look beyond short-term rewards….Its 184 pages are an urgent, accessible call to action, making a case that all is interconnected, including the solutions to the grave environmental crisis.

Perhaps we will do nothing about climate change until it’s too late. Last year was the warmest since records have been kept. This year is on track to be even warmer. But the climate isn’t changing fast enough to generate concerted global action. Short of a message from on high (from much higher than the sky), there may be nothing that will act as a sufficient catalyst. For now, however, Pope Francis has done his part.

Here are the first paragraphs of Laudato Si’:

1. “LAUDATO SI’, mi’ Signore” – “Praise be to you, my Lord”. In the words of this beautiful canticle, Saint Francis of Assisi reminds us that our common home is like a sister with whom we share our life and a beautiful mother who opens her arms to embrace us. “Praise be to you, my Lord, through our Sister, Mother Earth, who sustains and governs us, and who produces various fruit with coloured flowers and herbs”.

2. This sister now cries out to us because of the harm we have inflicted on her by our irresponsible use and abuse of the goods with which God has endowed her. We have come to see ourselves as her lords and masters, entitled to plunder her at will. The violence present in our hearts, wounded by sin, is also reflected in the symptoms of sickness evident in the soil, in the water, in the air and in all forms of life. This is why the earth herself, burdened and laid waste, is among the most abandoned and maltreated of our poor; she “groans in travail” (Rom 8:22). We have forgotten that we ourselves are dust of the earth (cf. Gen 2:7); our very bodies are made up of her elements, we breathe her air and we receive life and refreshment from her waters.

Nothing in this world is indifferent to us.

The entire text is here.

Garry Wills on Who’s Afraid of the Pope

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Garry Wills is one of America’s leading intellectuals. He’s now 80 years old and has had a brilliant career, but he’s still going strong. From the New York Review of Books blog:

Now, as the pope prepares a major encyclical on climate change, to be released this summer, the billionaires are spending a great deal of their money in a direct assault on him. They are calling in their chits, their kept scientists, their rigged conferences, their sycophantic beneficiaries, their bought publicists to discredit words of the pope that have not even been issued: “He would do his flock and the world a disservice by putting his moral authority behind the United Nations’ unscientific agenda on the climate,” they say. They do not know exactly what the pope is going to say in his forthcoming encyclical on preserving God’s creation, but they know what he will not say. He will not deny that the poor suffer from actions that despoil the earth. Everything he has said and done so far shows that Francis always stands for the poor.

Those who profit from what harms the earth have to keep the poor out of sight. They have trouble enough fighting off the scientific, economic, and political arguments against bastioned privilege. Bringing basic morality to the fore could be fatal to them. That is why they are mounting such a public pre-emptive strike against the encyclical before it even appears…..

The real issue here is not science vs. ignorance, or the UN vs. xenophobia, or my 97 percent of experts against your 3 percent. It is a case of the immensely rich few against the many deprived poor. The few are getting much of their wealth from interlocking interests that despoil the earth. The fact that the poor get poorer in this process is easily dismissed, denied, or derided. The poor have no voice. Till now. If the pope were not a plausible voice for the poor, his opponents would not be running so scared. Their fear is a testimony to him.

More here.

A Neutral Observer Might Detect a Pattern Here

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Ijeoma Oluo, a Seattle writer, has been tweeting “Don’t Do That and They Won’t Kill You” advice since yesterday. New York Magazine helpfully provided an annotated list of the fatal encounters she’s described.

Much too often, the apparently dangerous and criminal behavior at issue seems to have been “Being in Public While Black”.

Do many cops really see black Americans as so much more lawless and threatening than the white Americans they meet up with?

Today I saw a link to the video below. It shows how unreliable direct perception can be. It’s called the McGurk Effect in honor of the scientist who discovered it. From Wikipedia:

The effect was discovered by accident when McGurk and his research assistant … asked a technician to dub a video…. while conducting a study on how infants perceive language at different developmental stages. When the video was played back, both researchers heard a third phoneme [a perceptually distinct unit of spoken language] rather than the one spoken or mouthed in the video.

A couple weeks ago, in Cleveland, two cops responded to a 911 call, which can be heard here. The person who called 911 said that someone in the park (“probably a juvenile”) was scaring people with a gun (“probably fake”). 

It isn’t clear yet what the 911 dispatcher told the two officers to look for, but the black 12-year-old with the authentic-looking pellet gun was shot as soon as they arrived on the scene. From the New York Times:

Tamir Rice was killed by a rookie Cleveland police officer who quit a suburban police force after his supervisors determined two years ago that he suffered a “dangerous loss of composure” during firearms training and was emotionally unprepared to cope with stresses of the job. The officer, Tim Loehmann, 26, shot the child within two seconds after his patrol car pulled up next to the boy.

The Cleveland police said the child, who had what turned out to be a replica gun that shoots small plastic pellets but looks like a semiautomatic pistol, was told to raise his hands, but instead reached to his waistband for the object. Surveillance video of the killing that was released last week showed, however, that the shooting happened so fast it was hard to know whether the officer issued any real warnings or whether the boy could have understood them if he did.

I wonder what the young cop who had been fired by another police department saw when he and his veteran partner drove into that park. I wonder what the more experienced officer saw. It’s possible, even likely, that they didn’t see the same thing. Whatever each of them saw, however, it’s clear that one of them shouldn’t have arrived in that park with a gun in his hand, ready to use it, given what he apparently perceived.