# What do a poker’s hand, the model of oligopoly and two prisoners have in common?

Consider this situation. Let’s say we have two people, prisoner A and prisoner B. They have committed some sort of crime, a theft, a heist or whatever. They are detained by the police as prime suspects. They are completely unaware of the fact that evidence against them is very weak which leaves the police in the condition of needing a confession from at least one of the suspects in order to get a conviction. According to the police officer the best way to act is to divide the two of them in isolated rooms and offer the same scenario: confess the crime and you’ll obtain a lighter sentence to prison.

The two prisoners have to face a huge dilemma, which is summarized in the upper figure. If A confesses but B remains silent, A will get a heavier conviction. In the same way if B confesses but A remains silent, B will end up with to jail. What will happen is that, scared by the possibility of the other prisoner’s confession both will confess getting a far heavier prison sentence than the one they would have got remaining silent.

This little “episode” is more known as the so called Prisoner’s Dilemma and it is one of the most classic examples of game theory.

Game Theory is the study of how people behave in strategic situations. The best examples are specific games of strategy such as poker and chess. The best way to play such a game depends on the way one’s opponent plays. Players must pattern their actions according to the actions and expected reactions of rivals.

It is not surprising that one of the cleaner applications of this kind of mathematical, tactical and logical reasoning is the explanation of subtle behavioral patterns in economic models as oligopoly, a system in which the market is controlled by very few powerful firms. The financial strategies at the base of short or long run decisions must take into account the possible reactions of the rivals, which act and react subsequently. Fair competition or unfair collusion may alter considerably the market equilibrium.

Cool, isn’t it?

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by Francesco Pochetti

# Car or Goat? The Monty Hall problem

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice? (Whitaker, 1990, as quoted by vos Savant 1990a)

Remember the awesome scene in the movie “21” starred by Kevin Spacey about him (Professor Rosa) asking Ben (Jim Sturgess) exactly the same question mentioned above?

Were you (as me!) among the ones who at the end of the scene kept staring the screen wondering “what the hell is going on here?”?

Well, if so take a look at the following post!

The above brain teaser is known among mathematicians and statisticians as the so called Monty Hall problem , named after the original host (Monty Hall) of an American TV game show who first mentioned the trick.

In the recalled “21” movie scene Ben answers Prof Rosa’s question claiming that changing door is indeed in his favor because the probability of getting a car after the host has opened a fake door switches from the 33,3% (1/3) of the beginning to the 66,6% (2/3). Is it true?

If you don’t want to get too much insights into the mathematical description you may be satisfied with the following image showing in a qualitative way the reasoning behind Ben’s answer. The player has an equal chance (1/3) of initially selecting the car, goat A or goat B. Suppose the car was behind door 1; then if he selects it, the host could open door 2 or 3 but in any case switching would turn into a lose for the player (switching loses = 1/3). If  instead the player selected door 2, then the host could only open door 3, meaning that switching would turn into a win for our player. The same would happen if the candidate selected door 3; in this case too he would win if he decided to change to the left door. This qualitative analysis shows that in two cases out of three changing own’s mind wins, resulting in a global probability of 2/3 = 66,6% against 1/3 = 33,3% of winning in case of switching door.

Now let’s turn into something a bit more sophisticated. Same problem, same solution, different but more rigorous path to get there.

We are going to tackle the teaser applying the Bayes Theorem about conditional probability which states that “the probability of event A given B is equal to the probability of event A and B divided by the probability of event B alone”. In order to fully understand what goes on behind the scenes let’s summarize the problem by the decision tree shown below.

The diagram has been built assuming the player would choose always door 1 as his primary decision and the upcoming discussion may be as well followed sticking to the image below which is a self explanatory figure of the above tree. The probability the car is hiding behind one of the three doors is exactly 1/3. We shall begin with the first top branch. Given that the car stays behind door 1 the host may decide to open door 2 or 3 with the same probability of 1/2 (remember that the player selected door 1 behind which there is the car, meaning the other two doors hide goats). The probability the host opens door 2 or 3 given the car is hiding behind door 1 and the player has selected door 1 is (1/3 x 1/2) = 1/6.

Now let’s move to the second branch. If the car stays behind door 2 and the player has selected door 1 then the host can open only door 3 with a probability of 1. This means that the  the probability the host opens door 3 given the car is hiding behind door 2 and the player has selected door 1 is (1/3 x 1) = 1/3.

The same reasoning holds for the third branch resulting in the fact that the probability the host opens door 2 given the car is hiding behind door 3 and the player has selected door 1 is (1/3 x 1) = 1/3.

Now let’s apply Bayes Theorem which states that $$P(A|B)=\frac{P(A \; AND \; B)}{P(B)}$$

In our case:

• A = the player wins by switching from door 1 to door 2 which is the same as the car is behind door 2.
• B = the host opens door 3.

Summarizing, we’re answering the following question “What is the probability the player wins switching door given his first choice was door 1 and the host opens door 3?“. Note that the result wouldn’t change if I asked the same question conditioning the probability with the host opening door 2. Which translated into Bayes notation is

$$P(car \, is \, behind \, door \, 2 \, | \, host \, opens \, door \, 3)=\frac{P(car \, is \, behind \, door \, 2 \, AND\, host \, opens \, door \, 3)}{P(host \, opens \, door \, 3)}$$

computing the probabilities helping us with the previous decision tree we have:

• P(car is behind door 2  AND host opens door 3) = 1/3
• P(host opens door 3) = 1/6 + 1/3 = 1/2

$$P(car \, is \, behind \, door \, 2 \, | \, host \, opens \, door \, 3)= \frac{\frac{1}{3}}{\frac{1}{2}} = \frac{2}{3} = 66,6\%$$

Here we are! Finally quod erat demonstrandum!

That’s it! Cool, isn’t it?

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by Francesco Pochetti

# What is the gambler’s fallacy?

Imagine you are in a casino at a roulette table waiting to gamble. You have been following the game for a while and you’ve noticed that the last six outcomes were black. Well, it is quite remarkable, isn’t it? The probability to get six outcomes of the same color at the roulette is 1/64, approximately 1,6%. The chance to get seven consecutive blacks is the half, 1/128 or better 0,8%. Figures never lie! You must be very unlucky to obtain seven black shots. Therefore you put all your paycheck on red. But… wait a second. Is that right?

Obviously not! What you are missing is something fundamental which is the fact that consecutive outcomes at the roulette table are independent events which means that knowing the outcome of one provides no useful information about the outcome of the other. This involves that the probability to get seven consecutive blacks is truly 1/128 but the probability to obtain a seventh black after the first six ones is no more that 1/2, as there is nothing preventing the ball to stop either on a red or a black spot.

Unsuspecting gamblers may convince themselves that the odds are in their favor whilst they are not! So, be careful!

That’s the gambler’s fallacy.  That’s it! Cool, isn’t it?

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by Francesco Pochetti

# Endocrine Disruptors: how we are poisoned by everyday chemicals

How many chemicals do we get in touch with every day? Are they safe? In which doses? What kinds of chemicals are they?

If you have ever tried to find an answer to the previous questions probably this is the right place to check it out. In order to be as rigorous as possible I report the transcript of the first part of a very interesting and together frightening video I found on the net on Earth Focus web page, which you can find here and which I embed hereafter. Therefore I limited myself to simply watching the video and carefully writing down what I heard.

The topic dealt is crucial and is about Endocrine Disruptors (ED), a class of compounds, well known to science, which tend to interfere with the biological processes at the base of hormonal control. Basically,  ED have a molecular structure which resembles very closely the one of the most important human hormones (testosterone, progesterone, estrogens…) ; this feature gives them the ability to deceive cellular receptors which cannot recognize the real hormones from the fake ones. The result is that even at very tiny doses these chemicals might be very dangerous, altering irreversibly the most basic physiological human processes.

The above video (which I highly recommend) has been built gluing together pieces of interviews from the highest world experts in this field, whom I list below, before pasting the transcript, and whom I report within the transcript itself in order to clarify the respective contributes.

• Andy Igrejas (National Campaign Director/ Safer Chemicals, Healthy Families)
• Theo Colborn, Phd (President & Founder, The Endocrine Disrupting Exchange)
• Erin Switalski (Executive Director, Women’s voices for the Earth)
• Cecil Corbin-Mark (Deputy Director, WE ACT)
• Sean G. Palfrey, MD (Clinical Professor of Pediatrics & Public Health/ Boston University School of Medicine, MA)
• Heather White (Executive Director, Environmental Working Group)
• Judith Robinson (Executive Director, Coming Clean)
• Mia Davis (Vice President of Health & Safety, Beauty Counter)
• Johanna Congleton, Phd (Senior Scientist,  Environmental Working Group)
• Linda S. Birnbaum, Phd (Director, National Inst of Environmental Health Sciences/ National Toxicology Program, NH)
• Julia Brody, Phd (Executive Director, Silent Spring Institute)
• Tracey Woodruff, Phd, MPH (Director, Program on Reproductive Health in the Environment/ University of California, San Francisco)

BEGIN OF TRANSCRIPT

“They are everywhere in our environment, in the air we breath, the water we drink, the food we eat, they are in everyday products we use for personal care and cleaning, they are in our furniture, our children toys and the products we use in gardening and agriculture and almost all of us have them inside our bodies.

Andy Igrejas “Chemicals right now according to the best evidence we have are contributing to the chronic disease burden in this country in ways that are substantial.”

Sean G. Palfrey “We are seeing increases clearly in certain kinds of illnesses, asthma is one, autism in another, ADHD (Attention Deficit Hyperactivity Disorder) is a third”

Theo Colborn “One out of every third child born today is going to have diabetes and if you are a minority it’s one out of two”

Andy Igrejas “Chemicals contribute to the incidents of leukemia”

Mia Davis “breast cancer, infertility”

Theo Colborn “alzhaimer’s and parkinson’s”

Tracey Woodruff “People are more obese […] than they were up to 20 years ago”

Judith Robinson “Child’s cancers are going on”

Linda S. Birnbaum “We’re seeing effects on sperm count in men […]”

Andy Igrejas “They are more of these bizarre heart effects particularly around male reproductive development”

Theo Colborn “If I were a parent I would be very concerned”

They were meant to make life easier and they do. Chemicals fight diseases […] and support manufacturing. They’re big business, a key stone of the us economy from consumer goods to high technology almost all aspects of modern life depend on the chemical industry. Chemical production in the US has grown 25 fold since World War II. It sales above 763 billion dollars in 2011. The chemical industry supports over 3 million US jobs and invest billions in the research and development. Our bodies take in […] chemicals every day and this exposure has consequences for out health, our safety and our future.

Andy Igrejas “There are 84 thousand chemicals that are legal for commercing in the US and could be used to make all kinds of things, going to the products we bring into our homes, our workplaces and they are basically unregulated”

Theo Colborn “And of course every year new chemicals are coming on the line that have not been fully tested”

Erin Switalski “There are almost 13000 chemicals that are used in cosmetics and just about 10% of them have actually been evaluated for their safety. We found lead in lipsticks, there is mercury out there in skin lightening creams. We have found phormaldeid in products”

Cecil Corbin-Mark “[…] products that people apply to their faces and their skin daily”

Sean G. Palfrey “Pesticides are clearly poisonous and it should be obvious to us that if they kill insects they are going to have the possibility of hurting us”

Judith Robinson “In our kitchen cabinet. If you open up the doors and you count up all the tin cans in there, all of them are going to be lined with Bisphenol A unless they are labeled that say they are not”

Sean G. Palfrey PCBs (Polychlorinated Biphenyls) might be in plastics, might be in cups, might be in containers we put in our microwaves, might be perfectly safe when they are first put on the shelf but quite dangerous once they start to break down”

Heather White “All we have is chemical companies that have created products that have contaminated literally every living thing on the planet”

Judith Robinson “I think that the corporations who are profiting from this really have run away with our system”

Heather White “Industrial chemical pollution begins in the womb”

Erin Switalski “Everything that we are bringing into our bodies if we choose to have children, we actually pass our rate on through to a developing child”

Mia Davis “Some of the chemicals we know can cross the placenta and enter the womb and have effects at incredibly tiny tiny doses”

Sean G. Palfrey “About ten years ago a seminal study was done on ten newborns cord blood. The cord blood as the baby was born contained several hundred toxic elements which terrified all of us”

Heather White “Chemicals like Bishenol A, many different classes of flame retardants, we found DDT and PCBs, […] chemicals that we interact with every day from consumer products”

We now know that along with the nutrients and oxygen that the mother supplies to the baby comes a […] toxic chemicals.

Sean G. Palfrey “We know that chemicals will affect younger children, fetuses, new born babies and young children in general more than older children and adults and the reason for that is that younger children and fetuses are developing much more rapidly, their organ systems are much more sensitive”

Erin Switalski “What science is starting to show now is that early exposure to toxic chemicals at critical points when a child is in the womb has effects later in life”

Endocrine disruptors are chemicals of growing concern, fetuses and children exposed to even minute amounts may develop a wide range of health conditions from diminished intelligence to cancers. Our endocrine glands produce hormones that regulate the basic processes of our body like metabolism, growth reproduction and development. Endocrine disruptors disturb how these processes work.

Johanna Congleton “Endocrine disrupting chemicals interfere with hormones signaling. Proper hormone signaling is very important for fetal development and for childhood development as well as sexual maturation. Therefore compounds that interfere with these processes could have very profound effects”

Linda S. Birnbaum “Many of these and other chemicals appear to be associated with lower IQs and/or behavioral problems in children”

Theo Colborn “If you look at what these chemicals can do to the brain we know now these chemicals are also interfering with how we process information”

Sean G. Palfrey “They affect our genetic outcome, they increase the possibility that we lose a baby, they change the activity of our hormones, our sex hormones in a variety of different ways”

Linda S. Birnbaum “We’re seeing children starting puberty at younger ages. So there are many little girls that have, for example, breast at the age of seven in the african american community and eight in the white community. This is too young for our children”

980 endocrine disrupting chemicals have now been identified. Among the most ubiquitous are a class of compounds called Phthalates, Bishpenol-A and flame retardants including PBDEs, chemicals so common that almost all of us have them inside our bodies.

PHTHALATES

Judith Robinson “So you may have vinyl floors, you may have vinyl shower curtains, you may have vinyl toys that your kids are using, […] leaching Phthalates which are known to be toxic into the environment where you get exposed”

Phthalates are in many common products, including food packaging, building materials and pharmaceuticals; they’re in our cars and even in new cars’ smell. They’re used in cosmetics to hold fragrance and health products to more effectively penetrate and moisturize the skin.

Julia Brody “We’re concerned about their effects on males, on baby boys…”

Johanna Congleton “We see problems with testicular development, problems with sperm development. They can be associated with a decrease in testosterone levels.”

Tracey Woodruff “So if you interfere with the testosterone levels they don’t quite go up all the way. In animal studies it has been shown to be linked to cryptorchidism, so undescended testicles and hypospadias, which is incomplete formation of the male reproductive organ”

Phthalates may also be feminizing boys; scientists found that Phthalates may be associated with a shorter anogenital distance, the distance between the genitals and anus, a subtle marker of feminization in boys. The American Chemistry Council which represents chemical manufacturers says Phthalates are among the most thoroughly studied family compounds in the world and have a history of safe use. But Phthalates are banned from children toys in more than 10 countries and the European Union. In the US 3 Phthlates were permanently banned from children toys […] in 2008 because of their potential to leach frel plastic if chewed or sucked.

Johanna Congleton “The worst actors have been taken out of children’s toys but they are still widely used in many other types of consumer products and a monitoring study showed that these chemicals are still showing up in people”

BISPHENOLA

[…]

Tracey Woodruff “BPA is of concern because it looks like an estrogen and it has been shown to have a weak estrogenic effect and so if you are exposed to a chemical that might interfere with your hormone levels, in this case estrogen, it can have effects particularly during development.”

Linda S. Birnbaum “And there are preliminary data that say that it may infact […] directly increase the risk of breast cancer in animal”

Julia Brody “If they are chemicals that affect the development of the breast even before birth, if they are chemicals that cause breast thumors in animals, these are chemicals that we want to be worried about and start thinking about reducing exposure”

In addition to breast cancer BPA may be associated with genetic damage and a wide variety of reproductive, methabolic, behavioral and developmental problems. It’s one of the top industrial chemicals in the world. About 6 billion punds of BPA are produced globally each year, earning manufacturers a profit of some 8 billion dollars.

Johanna Congleton “We’ve made some progress with eliminating BPA from infant products including infant formula packaging, baby bottles and plastic drinking cups.”

But BPA remains widely used in many consumer products from electronic to medial equipmentsand it’s in the resin of cans […] and in plastic bottles where it can leach into the food or liquid contents inside. The Food And Drug Administration, which has jurisdiction over food packagings says BPA is safe at the low doses that occur in food but many research and health organisations remain concerned about BPA’s impact on human health at current levels of exposure.

FLAME RETARDANTS

Over 1,5 million tons of flame retardants are used worldwide each year. They’re added to consumer products to meet flamability standards, though their effect remains questionable.

Judith Robinson “Any furniture that you have that has polyurethane in it, that is most of our furniture, may contain toxic flame retardants and those flame retardants don’t stay put in the foam, they leach out and they end up in the dust in our house where we are all exposed, in particular kids who are on the ground, low, picking things up with their hands in their mouth. They are exposed to that dust which is gonna have flame retardants chemicals in it”

There are many different kinds of flame retardants. Among the most studied are PolyBrominated Diphenyl Ethers (PBDEs). Scientists have linked PBDEs to a wide range of conditions from delayed development to learning problems and diminished intelligence. […] Two PBDEs, pentaBDE and octaBDE were taken out the US market voluntarily in 2004 because of growing health concerns. Production of PBDEs deca is in the process of of being terminated.

Linda S. Birnbaum “The problem with all PBDEs is that they are very persistent in the environment”

Johanna Congleton “The issue with PBDEs is that they’ve been replaced with other types of chemicals that may have very similar concerns and perhaps even the same mechanism action in terms of their ability to disrupt the endocrine system”

The flame retardants Clorinated Tris and Fire Master 550, which may be linked to DNA damage, cancer or neurological defects continue to be widely used in polyurethane foam and in a number of children’s products.

Linda S. Birnbaum “So I think that the whole issue of flame retardants is one for which there is some concern and I think the real question we should ask, and maybe we need to ask this more broadly about other kinds of chemicals as well, is do we really need them?

[…]”

END OF TRANSCRIPT [15:57]

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by Francesco Pochetti

# How does a photocopier work?

We all know the difference between an insulating and a conductor. Despite that there are also materials which, depending on their conditions, may change their main inner characteristics: photoconductors, for example, are insulating substances which, after absorbing light, turn into conductors. This feature is exploited by a procedure known as xerography, which is at the base of copying machines and laser printers. The working principle of photocopiers consists in creating an electric image of the to-be-copied document over the photoconductor. Some colored pigment particles (toner) are layered on the electric image in order to get stuck to a blank sheet of paper, reproducing the original document.

A thin layer of photoconducting material is applied to a grounded metallic belt.

1. The free photoconducting surface is electron sprayed by a metallic wire, as if a nebulizer covered it with paint. The electrons polarize the photoconductor and get stuck to it: the effect of the polarization is to form a collection of negative charges on the opposite face of the photoconductor, in contact with the metallic belt. This negative charge attracts a correspondent positive charge which gathers on the upper face of the belt.
2. At this point, the document is lightened up and its image is projected over the photoconductor. Its exposed areas become conductive and, as this surface has a smaller potential level compared to the ground, the electrons scattered over these regions are immediately grounded. The shadowed areas, instead, keep their charge: over the free photoconductor surface a negative charged copied image is created (whilst a correspondent positively charged picture is kept on the surface facing the metallic belt).
3. It is now necessary to transfer onto the paper the charged image. By a special brush device, some toner particles (plastic insulating dust containing colored pigments) get positively charged and approached to the photoconductor.  The toner, attracted by charged areas (negative), gets scattered according to the original picture.
4. In order to let toner particles detach from the photoconductor and attach to the paper, it is necessary to get rid of the electrostatic attraction. The photoconductor gets lightened again and the charged image gets erased. The positive toner particles are kept on the photoconducting layer, in correspondence to the original picture.
5. After that a previously negatively charged sheet of paper is pressed over the photoconducting layer. The toner particles gets attracted without modifying the original drawing.
6. The final image gets eventually pressed whilst the toner melted by proper heating. Before a new copy the photoconductor is lightened for a third time to wipe the residual electrons and cleaned, in the very end, from the not transferred toner.

That’s it! Cool, isn’t it?

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by Francesco Pochetti

# Why does an airbag inflate?

For years, seat belts have represented the unique real safety device in our cars. Despite its not being immediately accepted, eventually the seat belt demonstrated all its efficiency.

The same happened to the airbag, whose concept has been around for many years. Its invention goes back to 1952, by John W. Hetrick who submitted the patent the following year. The first use is remembered at the end of the sixties, together with the big improvements to the other components necessary to its proper functioning. After all the prototypes introduced and tested by practically all the biggest car companies, the first vehicle carrying this kind of innovation was the Oldsmobile Toronado in 1973, followed by other models produced by Buick and Cadillac. In Europe it was Mercedes Benz the first one to offer the accessory on its top cars in 1980. After a first period of indifference and skepticism the airbag briefly took over at industrial level, turning into one of the strongest safety devices on a vehicle. The National Highway Traffic Safety Administration estimates that the combination of an airbag plus a lap/shoulder belt reduces the risk of serious head injury by 85 percent compared with a 60 percentage reduction for belts alone.

But how does an airbag work? Why does it inflate? Well you can believe it or not but chemistry saves our lives!

Timing is absolutely crucial for the airbag to save a life. An airbag must be able to inflate and work properly in a few milliseconds after the first collision. Meanwhile, it has to be projected in order to be restrained from deploying when the accident is negligible. Therefore, the primary component of the system is a well calibrated sensor able to reveal front strokes and to generate an immediate inflation of the device. One of the simplest mechanism studied for the collision sensor is a steel little sphere which is free to slide inside a smooth pipe. The ball is controlled by a magnet or by a rigid spring, which reduces the movements of the sphere when encountering bumps or potholes. Nevertheless, when the car decelerates rapidly, as for example during a crash, the sphere moves fast to the front triggering an electric circuit.

When the sensor switches on the circuit, a tiny mass of sodium azide (NaN3) starts burning in a very fast reaction, developing nitrogen (N2). This gas fills a nylon or polyamide envelope, which inflates completely after only 40 milliseconds. Ideally the body of the driver should not hit the airbag during the phase of inflation but just after, when it is beginning to lose pression. Otherwise the surface of the envelope would be too hard and may hurt the driver.

Inside the airbag there is a gas generator containing a mixture of NaN3, KNO3, and SiO2. When the car undergoes a collision, a series of three chemical reactions occur inside the gas generator. These reactions produce gas (N2) to fill the airbag and convert NaN3, a highly toxic substance, to harmless sodium and potassium silicate, a major ingredient of glass. Sodium azide (NaN3) can decompose at 300oC to produce sodium metal (Na) and nitrogen gas (N2). The signal from the deceleration sensor ignites the gas-generator mixture by an electrical impulse, creating the high-temperature condition necessary for NaN3 to decompose. The nitrogen gas that is generated then fills the airbag. The purpose of the KNO3 and SiO2 is to remove the sodium metal (which is highly reactive and potentially explosive) by converting it to a harmless material.

First, the sodium reacts with potassium nitrate (KNO3) to produce potassium oxide (K2O), sodium oxide (Na2O), and additional N2 gas. The N2 generated in this second reaction also fills the airbag, and the metal oxides react with silicon dioxide (SiO2) in a final reaction to produce silicate, which is harmless and stable. (First-period metal oxides, such as Na2O and K2O, are highly reactive, so it would be unsafe to allow them to be the end product of the airbag detonation.)

Well… as I said chemistry saves lives!

That’s it! Cool, isn’t it?

(Some information summarized from “Gas Laws Saves Lives: The Chemistry Behind Airbags”)

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by Francesco Pochetti

# Why does Aurora Borealis occur?

One of the most spectacular phenomena in nature is without doubt the amazing games of light, shades and colors called Aurora Borealis and Australis, depending on which of the two poles it is perceived at.

Those who live at the extreme north and south of Earth might at times experience this colored spectacular lights shimmering across the night sky. But what makes these lights  appear?

Well, it may sound weird but everything begins from the sun.

The temperature above its surface is millions of degrees Celsius. At this temperature, collisions between gas molecules are frequent and explosive. Free electrons and protons are thrown from the sun’s atmosphere by its rotation and escape through holes in the magnetic field. Blown towards the earth by the solar wind, the charged particles get in contact first of all with our planet’s magnetic field which may be thought as been generated by a giant rectangular calamite positioned at the centre of the Earth. The structure of a rectangular calamite’s magnetic field is well known and is based on closed field lines getting out of the south pole and entering the north one. Exactly the same happens on Earth where we have to imagine a giant magnetic shield protecting the whole planet surface, except for the source (south pole) and the pit (north pole) of the field lines which are necessarily more exposed.

The charged particles scattered all around by solar wind are largely deflected by the earth’s magnetic field. In particular these charges are trapped by the force of the magnetic field and they start following the force lines being channeled either towards the south or the north pole.  Therefore some particles enter the earth’s atmosphere and collide with gas atoms or molecules at various heights. These collisions  excite gas particles causing them to light up. Sounds something similar to phosphorescence…

What does it mean for an atom to be excited? Atoms consist of a central nucleus and a surrounding cloud of electrons encircling the nucleus at increasing distances from the centre. When charged particles from the sun strike atoms in Earth’s atmosphere, electrons move to higher-energy orbits, further away from the nucleus. Then when an electron moves back to a lower-energy orbit, in order to lose the amount of energy it has gained, it releases a particle of light or photon. The color of emitted light depends on the atom and on the size of the inner electron’s jump, but the result is absolutely amazing as it involves billions and billions of particles emitting light at the same time.

What happens in an aurora is similar to what occurs in the neon lights we see on many business signs. Electricity is used to excite the atoms in the neon gas within the glass tubes of a neon sign. That’s why these signs give off their brilliant colors. The aurora works on the same principle – but at a far more vast scale.

The aurora often appears as curtains of lights, but they can also be arcs or spirals, often following lines of force in Earth’s magnetic field. Most are green in color but sometimes you’ll see a hint of pink, and strong displays might also have red, violet and white colors. The lights typically are seen in the far north – the nations bordering the Arctic Ocean – Canada and Alaska, Scandinavian countries, Iceland, Greenland and Russia. And of course, the lights have a counterpart at Earth’s south polar regions.

The most common auroral color, a pale yellowish-green, is produced by oxygen molecules located about 60 miles above the earth. Rare, all-red auroras are produced by high-altitude oxygen, at heights of up to 200 miles. Nitrogen produces blue or purplish-red aurora.

Several fascinating  myths and legends are connected to the phenomenon of auroras.

In Finnish, the name for the aurora borealis is “Revontulet”, which literally translated means “Fox Fires.” The name comes from an ancient Finnish myth, a beast fable, in which the lights were caused by a magical fox sweeping his tail across the snow spraying it up into the sky. The Lapps, or the Saami, a people who are a close relative ‘race’ of the Finns, who live in Lapland — that is, north of the Arctic Circle, in what officially are Northern Finland, Sweden, and Norway — traditionally believed that the lights were the energies of the souls of the departed. In Norwegian folklore, the lights were the spirits of old maids dancing in the sky and waving.  Several of the Eskimo tribes also connected the lights with dancing. Eskimos in Eastern Greenland attributed the northern lights to the spirits of children who died at birth.

That’s it! Cool, isn’t it?

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by Francesco Pochetti

# Why do we slide on ice?

Have you ever wondered why we are able to slide on ice? For example why can we sky or skate? Why do we slide on ice and not on other smooth surfaces?

Well, the reason is quite simple and it is completely contained in the above image representing the so called water’s phase diagram.

Phase diagrams show the preferred physical states of matter at different Temperatures (abscissa – °C) and Pressure (ordinate – bar). Within each phase, the material is uniform with respect to its chemical composition and physical state. At typical temperatures and pressures on Earth water is a liquid, but it becomes solid (ice) if its temperature is lowered below 0°C and gaseous ( water vapor) if its temperature is raised above 100°C, at the same pressure. Each line (phase line) on a phase diagram represents a phase boundary and gives the conditions when two phases may stably coexist in any relative proportions. Here, a slight change in temperature or pressure may cause the phases to abruptly change from one physical state to the other. Where three phase lines join, there is a ‘triple point’, when three phases stably coexist, but may abruptly and totally change into each other given a slight change in temperature or pressure. Under the singular conditions of temperature and pressure where liquid water, gaseous water and hexagonal ice stably coexist, there is a ‘triple point’ where both the boiling point of water and melting point of ice are equal.  A ‘critical point’ occurs at the end of a phase line where the properties of the two phases become indistinguishable from each other, for example when, under singular conditions of temperature and pressure, liquid water is hot enough and gaseous water is under sufficient pressure that their densities are identical. Critical points are usually found at the high temperature end of the liquid-gas phase line.

Analyzing a phase diagram it is generally possible to predict the thermodynamic behavior of the considered substance.

Water is a scientifically fundamental example of this kind of analysis. So, let’s think about what may happen on a skating rink. The temperature is obviously under 0°C. At this temperature and at the pressure of 1 bar the thermodynamically water stable phase is the solid one. There’s no doubt that there would be ice.

But exactly when an hypothetical skater puts the blade of its runner over the surface of ice the situation changes. Or better the pressure conditions change. This pressure variation involves only the ice surface below the blade of the runner. Actually, the skater applies a pressure on the ground with its weight, determining a global pressure increase over the considered ice area.

Looking at the above water’s phase diagram, it is clear that if we increase the pressure the temperature of water solidification (temperature at which water is converted to ice) decreases under 0°C. The natural consequence is that the skater’s weight makes ice melt under the runner’s blade, as in that conditions of pressure and temperature the thermodynamically water stable phase is the liquid one. This means that, actually, the skater is not sliding over ice but over a thin layer of water between the blade and the below ice! That’s exactly what happens with a skier!

Cool isn’t it?

GO BACK TO MR WHY!

by Francesco Pochetti

# Why does phosphorescence occur?

Ever wondered why the little stars glued on our rooms’ ceilings go on glowing after we’ve switched off the light? What about funny shirts or glasses which are visible at night despite darkness? Why does all this stuff happen?

Well the phenomenon which is behind this cool events is called phosphorescence and we’are about to get a little bit of insight on it!

To better understand what goes on behind the scenes when this phenomenon occurs we have to ask ourselves a simple but fundamental question. What does it happen when a material is exposed to light? Which, in a more basic form, could be reasked in the following way:  what does  happen when a molecule is exposed to light?

Nice one!

Without getting into a too detailed analysis of the events we could simply answer the question in this way: the considered molecule absorbs the incident light. Or better, considering that a light beam consists in “little energetic packages” called photons, we should say that when a beam of photons bombs a material’s surface, the inner molecules absorb light in the form of “energetic particles”. The primary consequence of this absorption is that the molecules which were hit increase their internal energy. This energy, however, cannot be kept forever by the molecular system. In general it is quite immediately released by the molecule. This phenomenon is extremely fast and we could never appreciate it to the naked eye!

But let’s see a little bit more in detail what happens inside the molecule right after a photon absorption. There is a huge amount of extremely complex phenomena which are triggered by the absorption of light; all of them can only be explained using quantum mechanics.

Nevertheless it is still possible to have an idea of what’s going on in the following way. We first have to accept that each molecule has only well defined accessible energy levels, which means that everything hitting the system won’t automatically be absorbed. We can imagine the reachable energy levels of a molecular system as a building’s several floors. We have also to imagine that these floors are connected one to the other by an internal lift, which lets us reach them from the bottom to the top, and that, in the meantime, we can only use the stairs to go down. That’s it? Absolutely not! There’s another complication. While going down we cannot necessarily access to each floors, as if we had a direct access from the fourth floor to the first one but in order to pass from the third to the second we found a closed keyless door. Forbidden transition there!

Our molecule can be compared to a young man living on the ground floor of this imaginary building and our absorbed photon as a sort of nutritional supplement giving the weak young man some energy to stand up and climb the building to higher floors!

Ok.. So, what does happen after a molecule has absorbed (the right amount of) energy?

Our young man can now stand up and, completely revitalized, takes the lift till the floor allowed by the amount of acquired energy. That’s exactly (more or less!) what happens to a molecular system. It absorbs a photon whose energy excites the molecule to defined level. And what about the energy release?

Our young man has to descend back to the ground floor in order to lose all he has acquired. That’s not easy at all because there is the probability for him to find a forbidden path from a floor to an other. A closed door. What then? Theoretically he should stop and stay there, hopeless. Practically he could, for instance, force the door and access the forbidden transition. Obviously it would not be so fast at all. He would need time to open a passage and finally crash the door. Probably plenty of time. But finally he would succeed and he’d be able to go back to where he began. The ground floor!

After this awesome little story we are able to answer the first real question. Ever wondered why the little stars glued on our rooms’ ceilings go on glowing after we’ve switched off the light?

Here’s the answer: when we turn the light on, the stars begin absorbing energy. Or better the molecules inside the material start absorbing photons and get excited to a well defined molecular energy level. Immediately after they try to release this energy but it may happen that the system, attempting to go back to the ground floor, finds itself stuck at a particular energy level. Quantum mechanics reads that, in theory, there are some forbidden transitions. No way to pass! In practice, however, the molecule succeeds in forcing its passage to a lower molecular energetic level. Generally, this operation requires plenty of time, which means that our little star on the ceiling goes on glowing for minutes or hours after its first absorption.

When we switch off the room’s light we will be able to clearly see the phosphorescent star which is slowly releasing the absorbed energy  in the form of light! Phosphorescence! That’s it!

Cool isn’t it?

GO BACK TO MR WHY!

by Francesco Pochetti

# Why does a microwave oven heat so quickly?

Have you ever wondered why we are able to cook food so fast in a microwave oven?
Why is it so convenient in terms of time to use it instead of a classic oven?

To discover what lies in the backend of a microwave oven let’s start from its main components. This kind of oven contains three most important devices: a vacuum tube called a magnetron, which generates the energy that heats food, a waveguide hidden in the wall, to direct energy to the food and a chamber that holds the food and safely contains the radiation. The real cool stuff which is behind this revolutionary device is exactly this last one: the microwave radiation! After having been generated by the magnetron it is channeled by the waveguide and finally scattered into the main chamber of the oven.

From a physical point of view, as all the radiations, microwaves are nothing less than an oscillating electromagnetic field, the same as light, or radiowaves.

In principle a microwave does not heat differently than any other type of heat device; at a molecular level we are dealing about an energy transfer that results in an increased motion of the molecules and eventually in a rise in temperature. Its unique feature comes as follows: in a traditional oven we heat food by placing the it inside a radiated chamber with hot walls which cause the outside of the meal to raise in temperature. The inside of the food cooks by the heat transfer taking place from the hot surface to the inside. In contrast, energy from the magnetron penetrates into the food which means that all its mass can cook simultaneously. But how does he do this?

Well our food is generally filled with water which is a funny molecule positively charged at one end and negatively charged at the opposite one. To give this molecule an energy we expose it to the electromagnetic wave generated from the magnetron; this radiation stimulates simultaneously all the water molecules it encounters on its path. The typical microwave electromagnetic field oscillates 2.450.000.000 times per second. Water will try to allign with the oscillating radiation of the electric field, whose very fast variations rock the molecule back and forth rapidly. Well, imagine for a second a water molecule trying desperately to find a stable position in space being punched 2.450.000.000 times per second! That’s a big deal! The natural consequence is that the molecular friction creates heat and the frentic motion destroyes hydrogen bonds which bind molecules to its neighborhood. All this incredibly fast stuff is eventually translated into a progressive, rapid and homogeneous cooking of our food!

Cool, isn’t it?

GO BACK TO MR WHY!

by Francesco Pochetti