The first thing to remember about probability questions is that everyone finds them mind-bending, even mathematicians. The next step is to try to answer a similar but simpler question so that we can isolate what the question is really asking.

So, consider this preliminary question: “I have two children. One of them is a boy. What is the probability I have two boys?”

This is a much easier question, though a controversial one as I later discovered. After the gathering ended, Foshee’s Tuesday boy problem became a hotly discussed topic on blogs around the world. The main bone of contention was how to properly interpret the question. The way Foshee meant it is, of all the families with one boy and exactly one other child, what proportion of those families have two boys?

To answer the question you need to first look at all the equally likely combinations of two children it is possible to have: BG, GB, BB or GG. The question states that one child is a boy. So we can eliminate the GG, leaving us with just three options: BG, GB and BB. One out of these three scenarios is BB, so the probability of the two boys is 1/3.

Now we can repeat this technique for the original question. Let’s list the equally likely possibilities of children, together with the days of the week they are born in. Let’s call a boy born on a Tuesday a BTu. Our possible situations are:

▪ When the first child is a BTu and the second is a girl born on any day of the week: there are seven different possibilities.

▪ When the first child is a girl born on any day of the week and the second is a BTu: again, there are seven different possibilities.

▪ When the first child is a BTu and the second is a boy born on any day of the week: again there are seven different possibilities.

▪ Finally, there is the situation in which the first child is a boy born on any day of the week and the second child is a BTu – and this is where it gets interesting. There are seven different possibilities here too, but one of them – when both boys are born on a Tuesday – has already been counted when we considered the first to be a BTu and the second on any day of the week. So, since we are counting equally likely possibilities, we can only find an extra six possibilities here.

Summing up the totals, there are 7 + 7 + 7 + 6 = 27 different equally likely combinations of children with specified gender and birth day, and 13 of these combinations are two boys. So the answer is 13/27, which is very different from 1/3.

It seems remarkable that the probability of having two boys changes from 1/3 to 13/27 when the birth day of one boy is stated – yet it does, and it’s quite a generous difference at that. In fact, if you repeat the question but specify a trait rarer than 1/7 (the chance of being born on a Tuesday), the closer the probability will approach 1/2.

Which is surprising, weird… and, to recreational mathematicians at least, delightfully entertaining.

{ Magic numbers: A meeting of mathemagical tricksters | NewScientist | Continue reading }

photo { Bill Owen }

{ Ali Bosworth }

If you have an imagination, you don’t have to be the protagonist in H. G. Wells’ The Time Machine to travel through time. If you’ve ever eagerly awaited (or painfully dreaded) an upcoming birthday, recalled winning the lottery (don’t you wish), or fantasized about eating lunch while listening to your teacher drone on about why the river in the novel symbolizes the birth of modern civilization, you’ve mentally traveled through time.

Mental time travel is what got me through some of my postdoctoral days; watching spots (proteins) move across a computer screen was usually less than riveting. Besides alleviating boredom, the ability to use past experience (retrospection) to predict future scenarios (prospection) is extremely useful; you’ll be far more careful about when and where you leave your bicycle outside if it gets stolen.

{ National Association of Science Writers | Continue reading }

photo { Richard Kalvar }

Anyone pondering the future of television programming and related business models had better talk to my son Carson.

At the ripe old age of 18 months, he’s already a veteran iPhone and, now, iPad user. Having watched Carson control his exploration of media for nearly six months, I’m now convinced that there is no future for passive video consumption on any device — at least not once marketers become interested in him.

This isn’t going to be a gradual shift. This isn’t about migrating video to internet connected TVs or other devices. This definitely isn’t about moving some media dollars to support a schedule of :30s on Hulu or a home page roadblock on YouTube.

This is about how a generation feeding on absolute control and connectivity will have a completely different perception of media overall, and video in particular. The ramifications for programming and advertising are far more significant than anyone inside the current ecosystem is prepared or equipped to address. (…)

Here’s what we’ve found most interesting: While our son still has some tolerance for passive video watching on a television or mobile device, when given the choice, he almost always chooses the interactive experience. (…) I suspect that my son and other children of his generation will demand a seismic shift in programming — from static, passive video to immersive, interactive and intertwined content available on-demand and on any device.

{ Mike Henry/AdAge | Continue reading }

photo { Bill Owens }

The claim that “no one understands quantum mechanics” is often attributed to Richard Feyman, who said that to illustrate the perceived “randomness” that is at the heart of quantum mechanics and the Copenhagen Interpretation of QM. The unfortunate consequence of this phrase is that we now have people using it to claim that we know NOTHING about QM, and that no one understands it.

Without even going into what QM is, let’s consider the following first and foremost: we have used QM to produce a zoo of devices and techniques ranging from your modern electronics to medical procedure such as MRI and PET scans, etc. Already one can question whether this is a symptom of something that no one understands? When was the last time you place your life and the lives of your loved ones in something that NO ONE understands? That is what you do when you fly in an airplane or drive in a car that nowadays use modern electronics. All of these depend on QM for their operations!

The issue here is what is meant by the word “understand”. In physics, and among physicists, we usually consider something to be “fully understood” when it has reached a universal consensus that this is the most valid description of a phenomenon. We say that we understand Newton’s Laws because it is well-tested and we know that it definitely work within a certainly range of condition. (…)

So in physics, the criteria to say that we understand something is very, very strict. It requires a well-verified theory that matches practically all of the empirical observations, and a general consensus among experts in the field that agree with it. This means that in many instances, physicists would tend to say that we don’t understand so-and-so, because there are many areas of physics that haven’t been fully answered, verified, or have reached a general consensus. To us, this does not allow us to say that we have understood it. But it certainly does not mean we know NOTHING about it. (…)

Do we understand QM? Damn right we do! Do we understand it COMPLETELY? Sure if what we mean by “completely” only includes things that we can test and measure. QM is THE most successful theory of the physical world that human has invented up to now and no experimental observation so far has contradicted it. So that alone is a very strong argument that we DO understand QM. However, if we ask if we understand how QM comes up with all the correct predictions of what nature does, or if there’s anything underlying all the QM’s predictions, then no, we don’t. (…)

I’ve been known to reply, whenever I get another question such as this, that we understand QM MORE than you understand your own family members. Why? I can use QM to make QUANTITATIVE predictions, not just qualitative ones, and make these predictions uncannily accurate. When was the last time you can do that with your family member consistently, day in, day out, a gazillion times a second? We use QM to do that and more.

{ Physics and physicists | Continue reading }

artwork { Joseph Beuys }

{ Simen Johan }

White men with brown eyes are perceived to be more dominant than their blue-eyed counterparts. However, a blue-eyed man looking to make himself appear more dominant would be wasting his time investing in brown-coloured contact lenses. A new study by Karel Kleisner and colleagues at Charles University in the Czech Republic has found that brown iris colour seems to co-occur with some other aspect of facial appearance that triggers in others the perception of dominance.

Sixty-two student participants, half of them female, rated the dominance and/or attractiveness of the photographed faces of forty men and forty women. All models were Caucasian, and all of them were holding a neutral expression. Men with brown eyes were rated consistently as more dominant than blue-eyed men. No such effect of eye-colour was found for the photos of women. Eye colour also bore no association to the attractiveness ratings.

Next the researchers used Photoshop to give the brown-eyed men blue eyes and the blue-eyed men brown eyes. The photos were then rated by a new batch of participants. The intriguing finding here was that the dominance ratings were left largely unaffected by the eye colour manipulation. The men who really had brown eyes, but thanks to Photoshop appeared with blue eyes, still tended to be rated as more dominant.

{ BPS | Continue reading }

photo { Richard Avedon, Billy Mudd, Trucker, Alto, Texas, May 7, 1981 }

{ Apexart, 291 Church Street, NYC }

{ Disney Villains by Lcslayer }

…being green really is tough, so tough that the color itself fails dismally. The cruel truth is that most forms of the color green, the most powerful symbol of sustainable design, aren’t ecologically responsible, and can be damaging to the environment.

“Ironic, isn’t it?” said Michael Braungart, the German chemist who co-wrote “Cradle to Cradle,” the best-selling sustainable design book, and co-founded the U.S. design consultancy McDonough Braungart Design Chemistry. “The color green can never be green, because of the way it is made. It’s impossible to dye plastic green or to print green ink on paper without contaminating them.”

This means that green-colored plastic and paper cannot be recycled or composted safely, because they could contaminate everything else. The crux of the problem is that green is such a difficult color to manufacture that toxic substances are often used to stabilize it.

Take Pigment Green 7, the commonest shade of green used in plastics and paper. It is an organic pigment but contains chlorine, some forms of which can cause cancer and birth defects. Another popular shade, Pigment Green 36, includes potentially hazardous bromide atoms as well as chlorine; while inorganic Pigment Green 50 is a noxious cocktail of cobalt, titanium, nickel and zinc oxide.

If you look at the history of green, it has always been troublesome. Revered in Islamic culture for evoking the greenery of paradise, it has played an accident-prone role in Western art history. From the Italian Renaissance to 18th-century Romanticism, artists struggled over the centuries to mix precise shades of green paint, and to reproduce them accurately. (…)

Green even has a toxic history. Some early green paints were so corrosive that they burnt into canvas, paper and wood. Many popular 18th- and 19th-century green wallpapers and paints were made with arsenic, sometimes with fatal consequences. One of those paints, Scheele’s Green, invented in Sweden in the 1770s, is thought by some historians to have killed Napoleon Bonaparte in 1821, when lethal arsenic fumes were released from the rotting green and gold wallpaper in his damp cell on the island of Saint Helena.

{ Alice Rawsthorne/NY Times | Continue reading }

images { Erwin Redl, Matrix II, 2000 | light-emitting diode installation }

{ A Personal Letter From Steve Martin | Thanks Daniel C ! }

President Obama has secretly sanctioned a huge increase in the number of US special forces carrying out search-and-destroy missions against al-Qaeda around the world, with American troops now operating in 75 countries.

The dramatic expansion in the use of special forces, which in their global span go far beyond the covert missions authorised by George W. Bush, reflects how aggressively the President is pursuing al-Qaeda behind his public rhetoric of global engagement and diplomacy.

When Mr Obama took office US special forces were operating in fewer than 60 countries. In the past 18 months he has ordered a big expansion in Yemen and the Horn of Africa — known areas of strong al-Qaeda activity — and elsewhere in the Middle East, central Asia and Africa.

According to The Washington Post, Mr Obama has also approved pre-emptive special forces strikes to disrupt terror plots, and has given the units powers and authority that was not granted by Mr Bush when he occupied the White House. (…)
The aggressive secret war against al-Qaeda and other radical groups has coincided with a surge in the number of US drone attacks in the lawless border region between Pakistan and Afghanistan, an al-Qaeda and Taleban haven, since Mr Obama took office.

Just weeks after he entered the White House, the number of missile strikes from the CIA-operated unmanned drones significantly increased, and the pattern has remained. In Iraq, US forces have killed 34 out of the top 42 al-Qaeda operatives in the past 90 days alone. (…)

The order also allowed for US special forces to enter Iran to gather intelligence for a possible future military strike if tensions over its alleged nuclear weapons programme escalate dramatically.

The seven-page document states that the surge is designed to build networks that could “penetrate, disrupt, defeat or destroy” al-Qaeda and other militant groups, and to “prepare the environment” for future military strikes by US and local forces.

{ Times | Continue reading }

Just as the Defense Department and its suppliers worry about dependence on foreign oil, they also must be concerned about growing needs — and potentially declining supplies — of rare earth metals.

Rare earth materials are used in commercial and military systems for their magnetic and other unique properties. They include rare earth ores, oxides, metals and alloys.

According to a recent Government Accountability Office report, worldwide availability of these materials may be limited to a few overseas sources, primarily China. GAO noted that the Defense Department is in the early stages of assessing its dependency on rare earth materials and is planning to complete a study by September 2010.

A potential disruption of supplies of rare earth metals would not only affect the U.S. military’s ability to produce high-end weapons, but would also jeopardize the nation’s adoption of green-energy technologies.

{ National Defense | Continue reading | Thanks Douglas! }

Over the past several months, many in the mainstream media have hailed the slight improvement in the U.S. real estate market as a “housing recovery”. But the truth is that the small improvement in the numbers was primarily due to a significant number of Americans attempting to squeeze their home purchases in before the huge home buyer tax credit expired at the end of April. Now that there is no more giant tax incentive, real estate professionals all over the United States are fearing the worst. Mortgage defaults and foreclosures are still at record levels, and a giant “second wave” of adjustable rate mortgages is scheduled to reset in 2011 and 2012. In addition, there are numerous indications that the U.S. economy as a whole is going to experience a dramatic downturn shortly, and if that happens it is going to be really bad news for the housing industry. So are we about to see “Housing Crash Part 2″? (…)

The following are 12 reasons why the U.S. housing crash is far from over:

{ Seeking Alpha | Continue reading }

{ It’s not often that a US president has cause to declare that, given the chance, he would sack the boss of one of the UK’s leading companies. | The Deepwater Horizon catastrophe uncannily mirrors the global financial meltdown that was triggered by the September, 2008 collapse of Lehman Brothers. | Thanks Douglas! }

Americans are getting increasingly anxious–and for good reason.

People are worried about the economy, and they should be. They have been told to expect a strong rebound from our deep recession. The usual pattern is that recoveries mirror the strength of the decline–the steeper the drop, the more vigorous the rebound. It isn’t happening. The latest employment report makes it clear that the economy is not adding jobs. State and local governments faced with declining revenues are being forced to cut employment, wages and services, and they are raising taxes wherever they can.

A little over a year ago the Obama administration passed a staggering $787 billion stimulus package designed to rescue the economy. More than half of that money has now been spent, and the economy is still just creaking along. But now people are realizing that there is a dark side to this spending orgy. It has to end, and then we have to pay the bill. If we need any reminders that the day of reckoning is coming we have only to look to Europe.

{ Forbes | Continue reading }

For years, almost nobody paid attention to the sky-is-falling alarms of Edward Hugh, a gregarious British blogger and self-taught economist who repeatedly predicted that the euro zone could not survive. (…)

But now that the European sovereign debt crisis is rattling world markets, driving the euro lower almost every day and raising doubts about the future of the monetary union, his voluminous musings have become a must-read for an influential and growing global audience, including policy makers in the White House.

{ CNBC | Continue reading | Thansk Douglas }

related:

Personal Bankruptcies Jump 9% In May, And The Outlook For The Year Has Been Jacked Up.

China bank adviser says property woes worse than US.

Europe’s financial woes will hit the global economy, warns the governor of the Australian central bank, Glenn Stevens.

Public Pensions Could Bankrupt California.

Venice forced to sell off dozens of historic palazzos in order to bolster fast-diminishing funds.

{ Bill Evans, 1966}

{ Ray Sawhill }

The darkness was like nothing I’d ever seen. I couldn’t see my hand in front of my face; after a while I could barely believe that my hand was there, in front of my face, waving.

That darkness is what I think about when I think of black. I was going to write, the color black, but as every child knows black isn’t a color. Black is a lack, a void of light. When you think about it, it’s surprising that we can see black at all: our eyes are engineered to receive light; in its absence, you’d think we simply wouldn’t see, any more than we taste when our mouths are empty. Black velvet, charcoal black, Ad Reinhart’s black paintings, black-clad Goth kids with black fingernails: how do we see them?

According to modern neurophysiology, the answer is that photoreceptors in our retinas respond to photons of light, and we see black in those areas of the retina where the photoreceptors are relatively inactive. But what happens when no photoreceptors are working—as happens in a cave? Here we turn to Aristotle, who notes that sight, unlike touch or taste, continues to operate in the absence of anything visible:

Even when we are not seeing, it is by sight that we discriminate darkness from light, though not in the same way as we distinguish one colour from another. Further, in a sense even that which sees is coloured; for in each case the sense-organ is capable of receiving the sensible object without its matter. That is why even when the sensible objects are gone the sensings and imaginings continue to exist in the sense-organs.

We “see” in total darkness because sight itself has a color, Aristotle suggests, and that color is black: the feedback hum that lets us know the machine is still on.

{ Paul LaFarge/Cabinet Magazine | Continue reading }

{ Google Books | Nietzsche, The Antichrist, 1888 }

My favorite ad ever, I think it was in Frontiers or one of the gay magazines in L.A., and it ran for weeks and weeks, it was a classified ad. It said, “Every night at 10 p.m., here’s my address, my door’s unlocked. Fuck me.” (…)

Well phone sex is something I’d never do for fear that someone was recording it. I have done it before in my life. But it’s the kind of thing that today I’d be very hesitant about. Because you can never have healthy phone sex. Who has phone sex and then says, “One day we are going to fall in love and grow old together”? It’s usually some kind of verbal abuse or something. (…)

Well I’d advise that if you’re a bear, don’t tell your parents. Parents shouldn’t have to accept that. “Mom, Dad, sit down. I have something to tell you.” Imagine their nervous look. “I’m a bear,” you know; and they do that. (…)

Let me tell you, I’m at an age where I’m starting to attract people who want daddies, but I’d be mortified to be thought of as someone’s daddy. What I’ve learned is that with anybody who wants a daddy, it isn’t because they’ve had a good relationship with their daddy. It’s to punish their daddy, and you are the vessel. (…) Otherwise they would date people age-appropriate, something I’m not very good at. (…)

I have a very, very nice life as a single man. I’ve had long-term boyfriends and we’ve lived together in the summer, but I’m really bad at living with someone. You’ve never seen my house. Who could live in it but me? I could see someone saying, “I think I’ll hang this up.” No you won’t. And I can’t stand television. One relationship almost ended because of it. I can’t stand having a television on in my house. I don’t care if I’m wildly in love. If they watch television, it’s a deal breaker. I’ll make them wear earphones. (…)

What is sex to Michael Jackson? All it is is taking out that limp polka-dot penis and dribbling a weak load somewhere. He’s not a top. To me, I don’t know if he’s guilty, but I taught in prison and had a lot of pedophiles in my class, and he certainly fits the profile of a child molester. 


{ Interview with John Waters | Butt magazine | Continue reading }

photo { via Bon Jane | Facebook }