Internet Resources on the Housing/Finanacial Crisis: II

I've spent a lot of time looking at and trying to understand the Financial Crisis that our country is in right now. A while back, I made a post on (multimedia!) internet resources for understanding the crisis -- in terms that the average person can understand. More recently, I posted about the impact of the Financial Crisis on Women's Health.

Well, I've bumped into a couple of new resources (that are continually updated!) to help with general understanding of the crisis -- how it happened and where we are now.

• from New York Times
• Credit Crisis: The Essentials; updated continuously
• The really helpful stuff is on the left-hand side of the page. At the top of the column, they post the latest headlines and developments about the crisis (and how politicians and companies are reacting), but if you scroll down a little to where it says "Overview," that's where the handy explanations of the crisis begin.
• The middle column of the page is dedicated to Multimedia, and has tons of videos, graphics, and charts.
• from Wikipedia
• Economic Crisis of 2008; updated continuously
• Gives an overview of the economy in 2008, beginning with Causes of the Financial Crisis, then its impact on the major countries of the world (starting with the U.S.) up to the present.
• Global Financial Crisis of 2008; update continuously
• This article is similar to the one above, though it is slightly more advanced, and gives a week-by-week breakdown of the crisis starting when the stock market crashed in September. This article is much more focused and intensive. (It's not as much of a general introduction as the others.)

And I can't stress this enough: If there is ever a word or idea that you don't understand in any article or conversation about the economy, search it in Wikipedia. Smart people who know what they're talking about are updating Wiki-pages on the Financial Crisis all time!

Gravity and Quadratic Equations

Intro
When we finished talking about Gravity last time, the astronauts on Apollo 11 confirmed Galileo's theory that Gravity causes all objects to accelerate at the same rate (regardless of weight or size).

Near the surface of the Earth, the acceleration of an object due to gravity is: 32 ft/s² (9.8 m/s²). You would read that as "Thirty-two feet per second squared" (or "Nine point eight meters per second squared"). But you might be asking: What is a second squared?

[Note: Remember that as you move farther and farther away from the Earth, it has less of a gravitational pull on you. That change is only very slight even when you are as far from the Earth as in an airplane. All the way out near the moon though...that's a different story.]

Another way to write 32 ft/s² is 32 ft/s/s, which you would read "Thirty-two feet per second, per second." We know that feet per second is just a regular old speed. A car driving 50 miles per hour (mph) can also be said to be going 34 ft/s; every second, the car moves forward 34 feet, and every hour, the car drives 50 miles.

Feet per second is how far something moves after one second. So, feet per second, per second is how much faster something moves after one second. An acceleration, then, is the change in speed. If I am holding a bowling ball (over the edge of a cliff) and let it drop toward the Earth -- which has an acceleration due to gravity of 32 ft/s² -- then the ball starts with a speed of 0 ft/s (at the moment I let go of it) and after 1 second of falling, the ball is going 32 ft/s.


So finally, we have reached our Quadratic Equation. The distance equation is:
X_final = X_initial + V_initial*t + (1/2)*A*t²Where X_final is the final location of an object, X_initial is its initial (starting) location, V_initial is the initial (starting) velocity, A is acceleration, and t is time.

Physical Meaning of the Equation
You may remember the old distance equation that you learned in Algebra I: D=R*T (ie Distance equals Rate times Time). In our quadratic equation, the old D is now called X_final; the old R is V_initial. Our new distance equation is the next logical step. It not only looks at something's speed and the amount of time it travels, but also where it starts and whether the speed is changing (by the acceleration).

Going back to our bowling ball example, we determined before that the bowling ball was falling at a rate of 0 ft/s at the moment the ball was released (assuming you don't throw the ball downward), 32 ft/s after 1 second, and then 64 ft/s after two seconds, and so on. Our quadratic equation, however, finds distance; we can use it to find how far the ball has gone after a certain amount of time.


Calculation Time!
When we're using our equation to find the distance fallen (after some period of time), we need to know the values for all the variables besides the one that we're interested in. So when we drop the ball over the cliff, let's say that

• Initial position is Zero (since the ball has not traveled at all yet)
• which means that, for our equation, X_initial = 0
• Initial velocity is also Zero (since we're not throwing the ball either up or down)
• so V_initial = 0
• We know that acceleration due to gravity from the Earth is 32 ft/s²
• which write as A = 32

Plugging these values into our equation, X_final = X_initial + V_initial*t + (1/2)*A*t² becomes X_final = 0 + 0*t + (1/2)*32*t², which we can rewrite as:
X_final = 16*t²This means that we can determine how far the bowling ball has fallen by simply multiplying the time it spends falling, squared, by 16.

Doing some quick calculation:

• After zero seconds, the distance is Zero (the ball has not moved).
• After 1 second, the ball has fallen 16 feet
• X_final = 16*t² = 16*(1 sec)² = 16*1 = 16 feet
• After 2 seconds, the ball has fallen 64 feet
• X_final = 16*t² = 16*(2 sec)² = 16*4 = 64 feet
• And on and on and on... (of course, this all assumes that the ball doesn't hit the ground first)

We can even plot this if we want:


A parablola! [Note: Remember that the physical motion of the ball, though, is in a straight line down.]

Looking at the Math
The parabolic shape of the graph comes as no surprise to us, since we know that X_f = (1/2)*A*t² + V_i*t + X_i falls into the standard form of a quadratic equation
y = A*x² + B*x + CThis difference is that, in the equation for gravity, we use t as our independent variable and X as our dependent variable.

There are so many questions that can be asked at this point. What if we threw our bowling ball straight up first? What if we shot it from a cannon? And what if the cannon were pointed at an angle away from the cliff?



Instead of trying to answer all those questions right now, check out this applet about Projectile Motion (aka Shooting Stuff Out of a Cannon). Try it with different sized objects at several angles. After you've played with it for a while, try to find some patterns. And why does wind-resistance ruin your perfect parabola?!

Khan Academy

My attention was recently directed to a website called the Khan Academy. It's a huge library of YouTube video-lessons on Math and Science, and I've got a feeling that they're going to change the way that I do things on this blog.

Check them out, if there's something Math-related that you're wondering about, this guy probably has a lesson on it.

You Could Do This for a Living!

I just read an article in the New York Times, called YouTube Videos Pull in Real Money. It primarily reports about Michael Buckley who had put clips of himself on YouTube for nearly a year -- mostly just making silly comments about celebrities -- when they offered to make him a Partner.

A Partner is a regular member of YouTube who posts videos like everyone else; the difference is that YouTube gets to put advertisements in his video, and in return Michael Buckley gets paid. A lot. Mr. Buckley makes more than $100,000 per year just from YouTube, and he quit his old job when the videos became more and more profitable.

Stories like this happen all the time. People doing what they love put it on the internet, and a big company offers them money just to keep doing it. (This happens with blogs too! *Nudge*Nudge* to any big companies reading this.)

So, the real question now is: What do you love to do?

Bloxor!

Women's Health and the Economy

You've probably heard a little (or maybe a lot!) about the Financial Crisis that has been happening in the United States over the past few months. The headlines in newspapers for the past two weeks have all been about American car companies trying to get some help from the government ($15 billion in help, that is). Just Thursday was a report that 533,000 jobs were lost in November (that's the biggest number for one month since 1974).

But in all these headlines and numbers, you only hear about companies and executives and politicians who are trying to make decisions. But what about the people? And how is the Financial Crisis impacting women?

In an answer to some of these questions, a new survey was just released from the National Women's Health Resource Center. It has some shocking news to report:

• 45% of women have skipped health care in the past year because the cost was too high.

Just stop to consider the fact that if you have two American women in a room together today, it is likely that one of the two of them decided not to receive some form of health care in the last year (whether it was a prescription or a doctor's visit or whatever) solely because of the price.

But even in the face of rising costs, mothers still have their priorities set:

• While 28% of women report putting off a visit to the doctor when they were sick because the cost was too high, only 4% report putting off a visit for their child for this reason.

[Note: After combing the study's raw data for clarity, I believe that the percentage who put off a child's visit to the doctor is 4% of women overall, not just 4% of mothers.]

Things aren't looking too bright in the immediate future though:

• Among women who have not skipped medical care for themselves or their families in the past year, 55% say that they would be somewhat or very likely to do so if the cost they had to pay out-of-pocket increased significantly.
• And at the same time: 76% of women expect their and their families' health care costs to increase in the next few years.

I paired these two items to highlight the fact that skipping health care could be a reality for 75% of women in America within just a few years. Health care's price has already risen above affordability for 45% of American women and another 30% expect it to happen to them too. This is a financial crisis if I've ever seen one. But the highest, most devastating cost of all isn't monetary: Financial stress is trickling down from adults to children.

From a September, (fantastic!) front-page article in the Wall Street Journal:

At a little under three years of age, Bailey Haag can't understand the turmoil on Wall Street. But last week, the little girl's brow furrowed and her face grew sad as she overheard her mother on the phone, reacting to a ripple effect of the nation's economic problems -- her father's layoff.

Although her mother, Claire Crawford Haag, had hoped to shield Bailey from stress, the child knew from her mother's voice that "it was not a good conversation," Ms. Haag says. Noticing her daughter's face crumple, Ms. Haag began fashioning in her head an explanation a small child could understand.

Amid fallout from the nation's worsening financial picture, many parents are trying to protect their children from worries about layoffs and financial hardship. But children are actually silent carriers of family financial stress, research shows. They're not only keenly aware of it, but it makes them more likely to behave badly or develop emotional problems. To help kids cope, psychologists and researchers say, parents need to communicate in ways they can understand, keep family relationships on track, and give children a role in helping solve family problems.

Children's mental health (and apparently, even their performance at school) is directly impacted by the level of stress in their household. Returning to the Women's Health survey from earlier, I'd like to point out that 43% of women are worrying more about their health (in the last year). This means that despite mother's attempts to shield their children's health from the economic downturn (remember from earlier, only 4% of women have skipped on their child's health care in the past year), a negative impact is still being made.

Job security is lower than ever -- which means that employer-based health insurance can be relied upon less and less -- as women's physical health deteriorates ever more quickly.

• 42% of women report that their health has gotten worse in the last five years -- the majority of whom (53%) blame stress
• In terms of health care, 16% of women say their health has gotten worse because they were unable to pay for needed health care, and others say it has gotten worse because they lost their insurance coverage (10%) or a good doctor (7%)

And apparently women have taken on more stress than men in the last few months, due specifically to the financial crisis. Again, from the Wall Street Journal:


Are those numbers so surprising? Women are still earning 80% of men's pay (that statistic from 2007), while close to 1 out of every 4 children in the US is living with a single mother.

This is what it means to be in the midst of a financial crisis. Banks on Wall Street losing their value at a record pace, car companies struggling to not go bankrupt: these are only pieces of the puzzle. What makes a recession into a crisis is when 3 out of 4 women anticipate skipping health care in the near future (1 out of 2 have already this year), when millions of children watch their parents lose jobs (533,000 jobs in November alone). It may have begun in the financial sector, but when it reached into our homes and took hold of our very lives, that was when it became a crisis.

Gravity

In 1969, when humans first landed on the moon (on the Apollo 11 mission), one of the first things they did was drop a feather and a hammer to test which would hit the ground first. Why do you think they were interested?

• What happens when you drop a hammer and a feather (at the same time, from the same height) here on Earth?
• Is there any difference between performing the experiment on Earth and on the Moon?

Pre-Galileo
Did you hear the name that the astronaut mentioned? It was Galileo Galilei's. (Galileo was a physicist-astronomer who lived in Italy from 1564-1642.) For thousands of years before him, people believed that Gravity was a mysterious force that made things fall toward the Earth -- and they believed that the heavier the object, the faster it would fall. But Galileo changed everything.

Before we look at Galileo's theory, let's consider where the "old" belief about gravity came from. When you drop a hammer and a feather at the same time (here on Earth), the hammer will always land first. And if you try the experiment with all different kinds of things, this is pretty much always going to be the case for a heavy object and a lighter one: The heavier object tends to fall faster. Scientists observed this phenomenon for thousands of years and came to the conclusion that gravity affected heavier objects more than lighter ones.

However, they were not conducting their experiments on the Moon.

Galileo
Galileo (without ever leaving the Earth) did experiments many different objects that fell from many heights and rolled balls with different weights down inclined planes. Eventually, he came to the conclusion that gravity accelerates all objects at the same rate, regardless of their weight.

That means that even here on Earth, a hammer and a feather should land at the same time (like on the Moon). So why don't they? The answer: Air.


You know how when you ride a bike, you feel a breeze on your face (even when there's no wind that day)? The air is standing still, but you are moving, so it ends up feeling like there is wind pushing against the direction you're trying to go. It's the same principle with the hammer and the feather. A light breeze isn't going to push a hammer around, but it'll carry a feather away easily.

In the case of a hammer/feather drop, the breeze is trying to push each object in the opposite direction of the way they are falling (like the "wind" pushes against the direction you are trying to ride your bike). So even though Gravity is trying to accelerate both the hammer and feather at the same rate toward the Earth, the "wind" is blowing them in the other direction. On the Moon though, there's no air, so the hammer and feather can freely accelerate.

Peg Solitaire

I cannot stop playing this game!


A "European" Peg Solitaire board
Peg Solitaire is like one-player checkers: you jump pegs (or -- in the case of our board at Making Waves -- marbles) to take them off the board, with the objective of having a single peg/marble remaining.

Sounds fairly easy right? You'd be surprised. And once you've got the game beaten, you can try all different kinds of starting positions.

(I grew up playing a simplified version of Peg Solitaire at a restaurant called Cracker Barrel where they used to leave the game board out at the tables to play while you wait for your food.)

And for those of you feeling particularly Math-y, there are a couple pages out there detailing strategies and analysis of the board.

The European Union Has Already Developed a Plan to Stop Using Fossil Fuels for Electricity. Where's Ours?

It's called the Supergrid. The idea is a simple one:

Globally, the best renewable resource is solar energy. [...] Every year each square kilometre of hot deserts [in North Africa] receives solar energy equivalent to 1.5 million barrels of oil.
[...]
Solar factories can tap into this using concentrated solar power (CSP) plants [which] use mirrors to concentrate sunlight to create heat which is used to raise steam to drive steam turbines and electricity generators. An area of just 127km x 127km covered with CSP plants would produce as much electricity as Europe is using now.

Two German scientists, Dr Gerhard Knies and Dr Franz Trieb, calculate that just 0.5% of the world’s hot deserts, if covered with CSP plants, could generate as much electricity as the world now uses.

Okay. Pause for a second. The sun is burning millions of miles away from the Earth and just giving us its energy whether we like it or not. Before now, deserts were of use to very few living organisms. Humans have figured for the first time how to take advantage of these vast expanses.

Quick math:

• 1 sq. kilometer of the Sahara Desert receives as much energy (in the form of sunlight) in the course of a year as is contained in 1.5 million barrels of oil
• The Sahara Desert is about 9 million sq. kilometers
• 9,000,000 sq. kilometers X 1,500,000 barrels of oil per sq. kilometer = 13,500,000,000,000 barrels of oil

• Every year, the Sahara Desert receives sun-light energy that's the equivalent of 13.5 trillion barrels of oil
• FYI: That's way more than the 7.3 billion barrels of oil used every year in the US

The Supergrid itself is planned to be a web of High Voltage DC lines that stretch over thousands of miles -- at some points, even underwater. It would interconnect different areas of Europe and North Africa, and the majority of power would be supplied by solar energy from the Sahara, however every different geographic region in the web would contribute its own form of renewable energy (eg coastal countries would contribute energy from wind turbines).

What makes the Supergrid plan attractive is the use of 1) Concentrated Solar Power (CSP) plants to produce the energy and 2) DC lines to transport the energy.

Concentrated Solar Power
This refers to a way of converting sunlight into electricity by reflecting it off curved mirrors (parabolic mirrors to be precise) toward a liquid to heat it up and eventually boil water (which in turn spins turbines that make an electric current). It is a technology that is in its last stages of development and already produces more energy than other renewable sources.


DC Power Lines
I don't want to go too far into the difference between AC (Alternating Current) and DC (Direct Current) power, though you should know that (more or less) all power lines in the world are AC. (And I'd like to point out that when you plug an AC/DC converter into a wall socket, it takes the AC electricity from the power lines and converts it into DC electricity because for whatever reason your electronic device requires it.)

What's important for the Supergrid is that AC is works well for carrying electricity over distances that are less than a few hundred miles -- and therefore all the power lines in our country were built as AC -- however DC is better when you want to carry electricity over thousands of miles. That means, unfortunately that a whole new set of DC power lines will need to be built across Europe.

The plan has been proposed by a group called E-Parliament. Spain, Morocco, Algeria, and Egypt are already beginning to lay the groundwork, and there has been support from leaders in France, Germany, and the Netherlands. The former U.S. Vice President Al Gore has also spoken in support of the plan.

So where's the US's Supergrid?
Right now, there is one CSP plant in the United States -- called the Solar Energy Generating Systems (SEGS), which is in California's Mojave Desert. There used to be another one -- called Solar Two, also in the Mojave -- but it was shut down in 2001. The vast majority of the US's electricity is produced by burning fossil fuels -- including coal, natural gas, and oil -- which produce tons of carbon emissions annually.

But there's still hope! Whenever you hear Obama talking about the need to update our nation's infrastructure, this is one of the things he's talking about. If America ever wants to employ a green system like the Supergrid, we need to build new power lines first. Then, in time, we may build larger and larger CSP plants that could power the whole US. We're on the cusp of a new world of energy.

Student Skills: Test-Taking

[Note: The links in this post go to helpful pages on each topic. Follow them!]

Before the Test
It almost goes without saying, but the first key to test-preparation is GENERAL ORGANIZATION. Time management -- and the development of your REVIEW TOOLS -- over the days and weeks ahead of a test is probably the most effective boost to both your grade and your test-taking confidence. Once you've gotten into a groove with your classes and have a feel for the teacher, you can even begin to ANTICIPATE TEST CONTENT.

Testing Well
When you sit down to a test, you want to be in an optimal state to retrieve information that's been stored away in your head for the past couple weeks. Studying helps, but on test day, it's all about your brain. This means getting your body and mind into a balanced state.

It starts with studying enough to be confident in the material (none of that TESTING ANXIETY) and even arriving early to the test but also doing things to keep your body on an even level: exercising in the days before the test, eating breakfast the day of, deep breathing/relaxing if you even start to feel overwhelmed by the test. If you can do these, then strategic TEST TAKING will be like second nature for you (especially on MATH TESTS).

Having a LUCKY MASCOT when you study and take the test doesn't hurt either.

Cramming
Cramming for a test is pretty much incompatible with a healthy state of mind for test-taking, however it is almost certain that you will have to do it at some point. (That's why I figure it's better to mention it than to pretend that it will never happen.)

If you do hit a time crunch there are a few thing that you can do as EMERGENCY TEST PREP: You have to start by trusting what you already know of the material and identify 3-5 main concepts that have come up in your class. Write them, along with a brief description of each -- then compare that description with your notes and textbook. This will help you to figure which concepts you have a firm grasp of and which you need to work on.

After the test you crammed for, of course, it will be time to work on your TIME MANAGEMENT.

Mid-Terms, Final Exams
The STRATEGY FOR EXAMS is kind of a combination of all of the suggestions above. It's about Time Management (starting about two weeks before the exam), eating healthy and exercising (even though you've got a time crunch since finals are coming up!), Test Preparation, and Testing Strategy.

Don't worry. You'll do fine.

Corn-Based Plastic

[Attention: The proper way to dispose of corn-based plastic products is in your green, curbside-pickup compost bin (or a compost heap if you have one in your back yard). If neither of these are options, then put them in a garbage can, rather than recycling bin.]

• In 2007, Americans produced 256 million tons of trash
• 31 million tons of it were plastic
  • Only 2.1 million tons of plastic were able to be recycled; the rest went to landfills

As people are trying to become more green and cut down on their waste, scientists around the world are trying to find ways to cut down on the amount of plastic that goes into landfills. (You may have heard the pseudo-fact that plastic bags take 500 years to decompose.) One promising way to go about this is by developing biodegradable plastics (plastics that break down easily in natural settings -- like a log decomposing in a forest).

What's the problem with the "old" plastic?
The traditional plastics that you and I are used to are developed from fossil fuels (ie oil). This means that there are a great deal of carbon emissions (aka "Greenhouse Gases") from extracting the oil from underground and processing it into plastic. Also, as the oil-based plastic breaks down (over those "500 years" in the landfill), they will continue to release Carbon Dioxide (aka CO₂; aka the main man-made Greenhouse Gas). And this all on top of the space that plastics take up in landfills.

To avoid all these greenhouse gases (and save on rising oil costs), scientists and companies are now developing new types of plastic -- made from things beside oil -- that can biodegrade quickly and without all the Carbon Dioxide. Many different plants are being examined for their potential to be made into plastics (I recently heard about grass-based plastics). In the United States, we grow a crazy amount of corn, and it's rapidly becoming the popular new plastic. (So far, I've especially seen them as disposable utensils and clear, thin cups.)


If it's made from corn, it's "green" right?
The good news about corn-based plastics is that they cause far less Carbon Dioxide to be released into the atmosphere. Heck, the plastic originates from a plant that takes Carbon Dioxide and converts it into Oxygen. (Remember photosynthesis from your Biology class?) Unfortunately, not all of the Carbon Emissions of traditional plastics can be avoided: many of the power plants that run the corn-plastic factories are still burning fossil fuels like coal.

The bad news is that even though this new type of plastic can biodegrade (as opposed to the oil-based plastic), it only does so under very specific circumstances. The temperature must be about 140 degrees, it must be in a Nitrogen-rich environment, and there must be decomposing matter surrounding it. (Burying your corn-plastic fork in the back yard is not enough! You need a compost pile.)

This means that if you toss a corn-plastic fork into a landfill, it will still sit for 500 years next to that oil-plastic bag. And if you try to recycle it, it will just contaminate the oil-plastic that our recycling system is designed for. (The recycling system, of course, can be changed if corn-plastics ever become very common, but it will be expensive and take time.) Fortunately, here in the East Bay, we have an excellent curbside-pickup compost system, in addition to recycling and garbage. That is where the corn-plastic you use needs to be thrown out.

Also, it should be noted that corn-plastics are not as strong as oil-plastics. (As I mentioned above, they are considered a "contaminant" when they mix in with oil-plastics at recycling facilities because they make the oil-plastic weaker.) At cool temperatures, both plastics have about the same strength, but corn-plastic starts to melt at a significantly lower temperature than oil-plastic. This means that on a day where the temperature gets above 100 degrees, leaving corn-plastics out in the sun is a very bad idea. Not only because the plastics become weaker, but because they are toxic to humans and may contaminate any food or water that they come in contact with. (Think about water bottles that sit for a couple hours by the benches at a baseball field.)

Just tell me already: Are corn-based plastics good or bad?
If you have a green curbside-pickup bin or a compost pile in your back yard, then by all means go for the corn-plastics. (If you don't, then the decision can be a little tougher.) I'll say this much: even though they're not perfect yet, alternatives to oil-based plastics are definitely a good thing. Right away, the corn-plastics can reduce the amount of Carbon Dioxide we produce. And in the coming years, we may find plastics developed from other plants that are less toxic as well (oil-plastics are toxic enough as it is).

What does "overweight" really mean, anyway?

Just this morning, I went to see a new doctor. As part of all the procedures that we went through, she weighed me and measured my height. I knew what dastardly tricks she was up to: My doctor was calculating something called my BMI -- short for "Body Mass Index." It's a very simple method of classifying people's body-types, typically used to determine possible health risks. Essentially, you take a person's weight and divide it by their height squared.

(Okay, it's slightly more complicated than that because you need to have the weight in kilograms and the height in meters, instead of pounds and feet like we use in America. Fortunately, some easy multiplication can change our units of measurement into the correct form.)

The formula for BMI is:

So, you take a person's weight (in pounds) and multiply it by 703. Then, divide that product by the person's height (in inches), squared.

This may seem confusing so far, but let's think about what the BMI is figuring out. It's looking at two things: weight and height. Where have you seen a height squared before? (Phrased differently: What happens when you multiply a length times itself?)

Area=a²
The Area of a Square is found as the length of one side squared. This is just like what the BMI tells us to do with a person's height: Mathematically, the BMI flattens and stretches out a human body into a square that's as tall and wide as the person's height.

But overall, BMI is the person's weight divided by the person's height squared. So what does that mean? Basically, it determines how heavy each little square inch of the person's flattened out body is; it's some number of pounds per square inch (Rather it's the number of kilograms per square meter).

Okay. Now that we know how to figure out a person's BMI, let's calculate one real quick: mine. As of this morning, I am:

• 5'9.5"= (5 feet X 12 inches) + 9.5 inches = 60 inches + 9.5 inches = 69.5 inches
• 193 pounds

So,

• We square my height:
• (69.5 inches)²=4830 inches²
• Read aloud, that's: "Four thousand, eight hundred and thirty Square Inches"
• And divide my weight (times that conversion factor) by the height squared:
• (193 pounds X 703)/4830 square inches = 28

But what the heck does "28" even mean?

The World Health Organization has a handy chart that it gives to doctors around the planet to figure out health risks for patients based on their BMI:

BMI	Classification
Less than 18.5	Underweight
18.5–24.9	"Normal" Weight
25.0–29.9	Overweight
30.0–34.9	Class I Obesity
35.0–39.9	Class II Obesity
Over 40.0	Class III Obesity

So, according to the WHO, I am Overweight. This basically means that I have a slightly increased risk for certain types of cancer and possible heart problems over people who have a "Normal" BMI. This is where the problems start.

For a person with my height to have a "Normal" BMI, I would have to weigh somewhere between 127 and 172 pounds. I'll admit, if I lost 20 pounds, I'd be a little better off -- although I'd be skinnier than looks healthy for someone with my frame. According to the BMI, however, 172 pounds is supposed to be my maximum weight. They're saying that I could even weigh down to 127 pounds and be "Normal." If I weighed 127 pounds, I would be a sickly little thing that gets blown around by the wind. Even my doctor would tell me to gain a little weight.

All types of groups are against the BMI system for various reasons: 1) It identifies one group of people as Normal... which implies that people outside of that group are Abnormal. 2) The "Normal" group isn't necessarily the healthiest for many reasons, including the fact that 3) it doesn't take into account much human variation.

(I'd like to point out, specifically: studies have shown that people in the "Overweight" and some in the "Obese I" range of the BMI have the lowest risk for some types of heart disease.)

There are much better systems out there, including the Waist-Hip Ratio. This system is also pretty easy to compute: Divide the length around of your waist -- up near your belly-button -- by the length around of your hips. Females should shoot for the ratio 0.7-0.8, and for males, the ratio should be 0.9-0.95. These are only rough figures, since more research still needs to be done. But, in fact, a new study just came out confirming that Waist-Hip Ratio is better as a health indicator than BMI. (They examined 359,387 different people and came to that conclusion!)

As my doctor weighed me this morning, I told her that I don't buy the BMI system and that I believe there are better ones out there. She responded: "Then, I won't tell you that you should lose a couple pounds."

Student Skills: Classroom Participation

[Note: The links in this post go to helpful pages on each topic. Follow them!]

The classroom is the space in which a teacher gets all their impressions of you. The first thing that has to be said is PAY ATTENTION! (The only way that I can ever pay attention is if I'm in the first row of the classroom. Any further than the second row, and my mind will be all over the place.) And why pay attention? So you'll be great at TAKING NOTES, of course. There are many different strategies for note-taking, but sometimes, it's important just to jot down a few of the buzzwords your teacher throws out. Knowing what strategy to use totally depends on the class and how much you think you need to work to retain the information.

There are also the ever important CLASSROOM DISCUSSIONS where you get to demonstrate your intellectual prowess and show a teacher what you're all about. Even if "Classroom Participation" is officially only a small part of your grade, performing well can make things in the class run a little more smoothly. In fact, there are lots of little things that you can do to INFLUENCE TEACHERS that will make them believe you are the most interested student in the class (even if it's not exactly true).

Heck, a teacher's high opinion of you might even translate into things like a little boost if you're on the borderline between a B+ and an A- or that extra day you need to finish an essay.

A New Particle?

Back in September, you probably heard about that new particle accelerator in Europe that lots of (uninformed) people believed was going to end the world. Well, it kind of broke down before we had the opportunity to accidentally make black holes that would swallow us up. (Actually the way it broke and needs to be fixed is kind of cool: the accelerator runs at about -450 degrees Farenheit and needs to be warmed up so people can go in the room to fix it.)

In a way though, that breakdown is good news for us, since that means that the United States' old particle accelerator is still the most powerful in the world (until next spring when the European one is fixed). And on top of all this our old busted particle accelerator may have DISCOVERED A NEW PARTICLE! There were no predictions about its existence -- though one of the lead scientists on the project thinks it might be related to a developing theory of dark matter.

The suggestion of a new particle is actually really controversial; it may well turn out that it was an old particle doing some new tricks for us. In fact, nearly a third of the scientists working on the project don't want their names included in an article that's coming out soon about their findings. It's way too early to know whether it was a new particle or some older one. Only time will tell.

[On a related note: Another group of scientists are searching for dark matter right now, deep in a mine in Minnesota. The article is really informative and can help you to understand what dark matter is all about.]

Playing with Functions

Comparing graphs of linear equations can be really helpful in trying to understand them, but just trying to graph them takes a really long time. Fortunately for us, someone out there wrote a Java applet (a simple program) just for us, called Slope Slider. The whole concept is that you can push the colored sliders left and right to easily change the slope and y-intercept.

The big questions to think about are:

• What happens to the slope when it's greater than 1 and getting bigger?
• What about the slope between 0 and 1?
• How different are the lines with slopes +10 and -10? What about +100 and -100?

[Note: When you're done with the "Slope Slider" check out this other applet that graphs functions for you. Typing in the function can be a little bit funky, since you have to use an asterisk (*) to do multiplication and a caret (^) to show that what follows is an exponent, but it can graph almost any function you want.]

Student Skills: Studying

[Note: The links in this post go to helpful pages on each topic. Follow them!]

Studying well doesn’t necessarily mean studying a lot; it means reading efficiently and being able to hold on to the information. Before anything happens you have to get in your zone. That means finding a space – both at a STUDY SPACE and in your head – where you can CONCENTRATE.

In that space, reading can be more like SKIMMING, instead of long and intensive. And I’ll give you a tip, there are tons of tricks to help MEMORIZE information, but the best way is to see it often. Instead of studying vocab for an hour the night before a quiz, try fifteen minutes a night for four nights; either way, it adds up to 60 minutes, but one will do you just a few points better.

And laid out in front of you, it often helps to see MULTIPLE SOURCES of information. A textbook has facts, but it can be dry…and limited. Maybe your teacher gave you a handout with a short story illustrating a point from the textbook or a class lecture that you surely still have the notes from. Heck, maybe someone made a youTube video out of that story. Getting a big picture can help hold together all the little details that you’re trying to memorize.

Student Skills: Time Management

[Note: The links in this post go to helpful pages on each topic. Follow them!]

The first thing that any student needs to do is get their PRIORITIES straight. But when you’re figuring them out, you have to be honest! You know plenty of kids who prioritize schoolwork over the rest of their lives – and that’s great, you get plenty of work done like that – but if you tend to take new MySpace pictures instead of practicing Spanish vocab, you have to start by admitting that it’s something important to you and that has to be in any schedule you make for yourself.

Schedules are really helpful to refer to both when you’ve got tons of work (and you need to figure out how you’ll fit it all in) and when your time can be more relaxed (which is when I tend to forget whatever is due). For Long Term planning, a WEEKLY SCHEDULE or MONTHLY CALENDAR to fill in are helpful – and the Weekly Schedule can help you find things like time slots to squeeze in a little extra review, during Exam Week. You probably know most of your usual DAILY SCHEDULE already, but writing it down can help you make your days more efficient.

Internet Resources on the Housing/Finanacial Crisis

• This American Life (radio show) episodes:
  
  1. 5/9/08: The Giant Pool of Money
     
     • Through that link, you can read a summary of the episode, download a transcript of it as a PDF or stream the audio to your computer -- or pay a dollar to download the audio, but who wants to do that?
  2. 10/3/08: Another Frightening Show About the Economy
     
     • For this episode, there's a summary, but you can only stream the audio or buy it-- no transcript to read available yet
  
  
• New York Times (newspaper) multimedia presentation:
  • The Debt Trap; videos, interactive charts, and newspaper articles about all the different people who are affected by debt and how they fall into it in the first place
  
  
• Washington Post (newspaper) slide show:
  • Anatomy of a Crisis; the slides are narrated, describing how the "Housing" crisis turned into the "Financial" crisis
  • Note: the narrator goes a little too fast if you're not already familiar with the events and the vocabulary he throws around

Black Turnout is Strong in Early Voting in the South

The usual way that people vote in a General Election (that's the name for an election that's nationwide) is by going to a "polling place" in their town where voting machines are all set up on Election Day. This year, our Election Day is November 4. These polling places are normally in a local school or library, and people go in and out of the place all day, whenever it is convenient for them, and it is usual to wait anywhere between 5 minutes and almost half an hour (depending on how quickly things are going).

There are other ways to vote, including Absentee Voting (which I just did today!), but this year, it has been especially popular to do Early Voting. Early voting is basically like going to the polling place on Election Day, except that you can turn in your ballot up to a month before the actual election -- and it gets counted early!

Part of the reason that this option is really popular this year is because more Americans are planning to vote than ever before in this Presidential election, and some people are worried that polling places will be overcrowded and that you would have to wait hours in order to vote.

An article just came out talking about exactly who is voting early this year,and according to it:

The Voting Rights Act of 1965 requires several Southern states to report racial breakdowns among voters, an effort designed to prevent discrimination. But North Carolina, Georgia and Louisiana are the only ones reporting that information as early voting is proceeding.

Here are the data they've turned in:

---------------------	North Carolina	Georgia	Louisiana
Black Voters (as % of Early Voters in 2008)	31%	36%	31%
Black Voters (as % of TOTAL Voters in 2004)	19%	25%	--
Black Population (as % of State Pop.)	21%	30%	31.7%

[Update (10/30/08): These numbers are changing every day, since Early Voting continues up to Election Day. In Georgia, Louisiana, and almost in North Carolina, the total number of Early Voters has doubled those in 2004 for each state. The percent of this year's black Early Voters in Georgia has dropped a point to 35%; in North Carolina, it's fallen four points to 27%. And in Louisiana, that percent has actually risen to 36%.

And there's a new page with raw data (that I assume will be updated daily) on Early Voter turnout in all 50 states.]

Check out general facts on voter registration and state populations at the US Census Bureau website.

Probability: Schrodinger's Cat

Quantum physics is probably one of my favorite things in the world. It is the point where Science begins to blend with Philosophy and Religion, examining the very fabric of the universe. You have to ask yourself questions about Time (What happened before the Big Bang?), Space (What would happen if you fell into that Black Hole?), and even the particles and atoms that make up your own body. I'm making it sound really out there, like it is a bunch of old scientists sitting around and talking about life, but really it is Math-based and requires lots of experiments.

Before our time, Physicists (the scientists who work on this stuff) used to study the world on a level that we could see and touch. For example, you may have heard the story of Isaac Newton coming up with his theory of gravity when an apple dropped from a tree and hit him on the head. Well, that was in the year 1666, and we've come a long way since then.

[Extra: In the 1800s, Physicists were all about electricity and magnetism (which were discovered to be related when a teacher, setting up for class accidentally set some electric wires near a magnetic compass).]

As technology developed in the early part of the 1900s, people could make more and more exact observations about smaller and smaller objects. Physicists started to find that when they looked at the very smallest things, they behave in strange and surprising ways. I'm not talking about small like an ant or even small like the cells you learn about in Biology class. Smaller. I'm talking about atoms and the things that make up atoms, called subatomic particles. (That prefix sub- just means smaller than; and particle is a fancy word for object or thing.

[Extra: For those of you who have taken Biology, there are about 100 trillion atoms in a single cell -- and coincidentally there are about 100 trillion cells in a human body.)]

A picture of a Helium atom: two Protons and two Neutrons stuck in the middle (called the Nucleus), circled by two floating electrons.

You may already know about some subatomic particles from your science class: The most common ones are Protons, Neutrons, and Electrons. In addition to being subatomic particles, these can also be called quantum particles -- this means that they are particles that act in crazy and unpredictable ways because they are so small (we'll talk about some of that unpredictability in a minute).

Now, you may be wondering why a person would be interested in looking at something so small. Einstein got interested because he liked to think about Philosophy. The United States government got interested in the 1930s and 40s, when it was discovered that atoms hold huge amounts of energy for being so small and that if you blew up a lot of them at the same time you would have a bomb much more powerful than dynamite -- This led to the atomic bomb. Computer companies got interested in the 1980s when they started making electrical circuits so small that they acted in ways that the scientists couldn't understand -- Those circuits and chips now power your computers and cell phones.

One of the big things that makes the subatomic world so hard for us to understand is that opposite situations can be true at the same time. Remember how I mentioned that a coin when it's flipped can only be heads or tails when it lands? Not so for quantum particles.

These particles are rarely found alone (they are usually part of a larger atom, and atoms are usually clustered together), but let's imagine for a moment that we could flip an individual Neutron as if it were a coin. You toss it up in the air and when it lands, you cover it with your hand. If this were a quarter, you would know that it was Heads or Tails under there, and you were just waiting to find out. But for the Neutron, it would actually be both Heads and Tails -- until you looked at it. Only when you lifted your hand would the Neutron decide to be Heads or Tails. The situation in which the Neutron is both Heads and Tails -- or any time that opposites are true -- is called "Quantum Superposition" (This is part of the joke from the LOLCats picture at the beginning of this post: "kwantumz sooperpozishin.")

If you feel confused right now, it's perfectly natural; this idea makes no sense to us. Here's an example of how it would be if Quantum Superposition were possible for things that are our size: You could be watching a basketball game on TV, and let's say that a player is shooting at the buzzer to win the game. The ball is just leaving his hand, and suddenly your house's power goes out. You now do not know whether the ball goes in or not, whether the player's team wins or loses. Therefore, the team both wins and loses; the ball went through the net and it bounced off the rim. The team might even be both moving forward in a tournament and eliminated from it. ...That is, until you check the scores the next day to find out what happened (like lifting your hand off the Neutron). It turns out that the ball went in, and the team only remembers having won the game (not both possible outcomes). Crazy, huh?

The question that most people ask at this point is: how do we know that the Neutron wasn't Heads the whole time it was under our hand -- the way that a quarter would be -- and we only just found out when we checked it? That's the thing about the Quantum world: until a particle is observed (by another particle or by humans with a microscope), it doesn't have to decide what any of its characteristics are. A Neutron is not like a baseball or a watermelon that is solid and well-defined -- it's more fluid than that. A sub-atomic particle does not even have to choose where it is until an observer forces it to decide.

A Physicist friend of Einstein's, Erwin Schrodinger (SHRO-din-jer), took these issues a step further with the thought experiment (an experiment that you just imagine), that people usually now call Schrodinger's Cat. In the experiment, there is a certain atom that has a 50% chance of "decaying" (which means that it shoots out some of its energy as a tiny amount of light) in the course of one hour. The atom is inside a box with a detector that will see if light is released from the atom. That detector is hooked up to a device that, if some light is observed, would release poison gas into another box that has a cat inside. Once an hour has gone by (since it was the time period for the 50% chance that the atom would decay) so the experimenter turns off the detector.

PETA had a field day with this one.

This situation is different from the examples of "flipping" a Neutron and the Quantum basketball game, because it mixes the subatomic world with our very large one. A Neutron, by itself, has pretty much no impact on anything, so who cares if it's Heads or Tails. The quantum superposition of the basketball game simply does not happen in our world. But there is a quantum superposition for an atom's decay, and a cat's life hangs in the balance. (It could have been any animal or living thing in that box, just so long as it was something large enough to see and touch.)

The question that Schrodinger asked was: Could the cat be both dead and alive? Remember, we said that the 50% chance of the atom decaying and shooting off light is like the probability that a coin will land Heads or Tails, except that the coin is both Heads and Tails until we check -- the atom both has decayed and has not decayed. Can the cat in the box be in a quantum superposition of "Alive" and "Dead"? [There you go, that's the punch-line to the picture at the beginning of the post.] If the experimenter opened the box and found that the cat was alive, the cat would only remember having been alive. And if it were dead, then when did it die? When the experimenter opened the box?

Schrodinger first asked these questions in 1935. The best answer that anyone could give for a long time was: Yes, there is in fact a period of time in which the cat was both dead and alive (not like a zombie, but both fully dead and fully alive), until the experimenter opened the box. However, this is not true. Physicists have since figured out that there is no Quantum Superposition for very large things. If the experimenter opened the box and found that the cat was dead, then the cat died at some definite point before the experimenter opened the box and even before having turned off the detector. Remember how we said that the Neutron was both Heads and Tails, until we observed it? Well, the observer doesn't have to be a human; the detector in the box counts too. So there was in fact a definite time (let's say 35 minutes into the hour of the experiment) when the light was released from the atom and the cat died. There was no time when the cat was both dead and alive. [Note that if the atom had been all alone, far away from any other particles, then it would have been in a superposition of both decayed and not decayed -- but this is not the case in our experiment.]

This is all to give a simple explanation of an advanced concept in Probability. I'd said in a previous post that even though there is a 50% chance of getting Heads or Tails on any given flip, you couldn't have a coin flip that was 50% Heads and 50% Tails; it is always forced to be one or the other. Well, with (unobserved) subatomic particles, both Heads and Tails happen all the time. You can flip that Neutron as many times as you want, but as long as you don't look at it, then it is both Heads Up and Tails Up, every time.

Mr. Narasimhan's blog

Mr. Narasimhan, who sits at the desk next to mine, has his own blog called Some Random Math Stuff. Check it out.

Probability: Dice, Coin Flips, and Life

The six-sided die is one of the simplest, commonest, yet most perplexing devices created by human hands. How does something so tiny defy all but the most general predictions? Just consider the fact that it inspires such awe in our society that there are laws surrounding their use. (I should probably mention that even teaching about dice is frowned-upon in our country; some textbooks only refer to dice as "random event generators" -- but we know what they really mean.) Instead of fearing the die, though, let's empower ourselves by working to understand it.

[Note: This post is pretty long, so for those with short attention spans, I'll summarize it for you right here.

1. Probability is given as the number of desired outcomes, compared with the number of possible outcomes. The probability of rolling a 3 on a die is 1:6, since there is only one face on the die with the number 3 and there are six possible faces that can land up.
2. Past random events do not influence future random events. Just because you rolled a 3 doesn't mean you will roll all the other numbers before you roll 3 again. You can easily roll two 3's in a row.
3. Probability can be thought of as our confidence level that a particular event will occur. If you flip a coin four times, it is not guaranteed that the coin will land heads up twice. But you can be 50% confident that it will.

If you have trouble understanding any of these or want to explore them more then check them out in the corresponding Parts 1, 2, and 3 below.]

Part 1: One Die
A regular die has six faces -- all labeled a different number, 1 through 6 -- and the weight of the die is evenly distributed. (Even distribution of weight means that no single side is heavier than the others. If one side were significantly heavier, it would tend to land face down more often than the other faces; this is what we call a "loaded" die.) Casinos go to great lengths (ie they spend a lot of money) to buy dice in which the weight is perfectly distributed.

So, for a perfectly fair die, what are the odds that I roll a 6? And is it any different from the odds that I roll a 2?

The second answer is: No, the odds of rolling a 2 and a 6 are identical. The numbers on a die are simply markings that label the sides -- it would be the same as if they were labeled by letters or different colors. The number on each face has no bearing on the odds it will be rolled, since all of the faces are equally likely (remember that the weight was evenly distributed in the die).

At this point, we say confidently that the probability of rolling a 6 is the same as a 2 (is the same as a 1, as a 3, etc), but what exactly is the probability that I roll a 6?

The way that we calculate the probability of an event's occurrence (in this case, the probability of rolling a 6) is we consider the total number of possible results and compare it with the number of results that we want. Considering a die, as it rolls in our hand, there are six possible sides that we may roll; it may land on the 1, the 2, the 3, the 4, the 5, or the 6 -- s0 6 possible outcomes, all of which are equally likely. Now, we ask what is the probability I roll a 6? Well, there is only one desired outcome out of six possible ones, so we say that the probability is 1:6 (which is read as "one-to-six" or "one-out-of-six" and which may also be written as "1/6").

As a side note, randomly producing numbers is one thing that computers are very good at, and there are many sites on the web that have Java and Flash applications to roll dice. I like this one, since it allows you to choose the number of dice you want, and if you set Results to "Session," then it will record the results of each roll you do. (The "Auto-Roll" button gives the results for however many rolls you type in the box, and setting Results to "Historical" shows the results for every roll that has been done on the website.) You can go there to test out all the stuff we're talking about here or just pick up some real dice of your own.

For contrast, let's say that you and I are playing a game where we roll a die to see who goes first (ie whoever rolls the higher number). I start and roll a 3. You have to roll higher than 3 to get the first turn, which means rolling either 4, 5, or 6. In this case, those are 3 desired outcomes out of 6 possible outcomes (I'm assuming here that you want to go first...). So, we say that the probability is 3:6.

Another way to come to this conclusion is figuring which are the desired outcomes (4, 5, and 6) and adding up their regular, old probabilities. The probability of a 4 is 1/6; the probability of a 5 is 1/6; the probability of a 6 is (once again) 1/6. So, summing them up:

• 1/6 + 1/6 + 1/6 = 3/6

And like the fractions that you're used to, 3/6 can be reduced to 1/2.

But what does a 1:2 probability mean? Or for that matter...

Part 2: What does a probability mean, in general?
Well, in a very technical sense, a probability simply gives you two pieces of information: the number desired outcomes and the number of total outcomes (...which is exactly what we said before). But that doesn't really tell us anything, does it? Consider this: The probability of rolling a 6 is 1:6. But I might roll a 4 twice before I roll the 6 that I'm waiting for. If both faces of the die were equally likely: does that defy the logic of our discussion? Shouldn't I have rolled 4 only once before the 6?

Not at all. You should make a mental note to yourself that past (random) events do not influence future (random) events. This is one of the hardest things to wrap your head around, and even the most brilliant mathematicians and scientists, poker players and craps shooters make mistakes all the time because they forget that simple rule. If we could use past throws to predict future ones, then you could figure out an easy system to win every time. Heck, the stock market would be a gold mine. What this all means is that the opening scene of Tom Stoppard's play "Rosencrantz and Guildenstern Are Dead" is perfectly possible (...however unlikely it may be).

In the scene, R. and G. are friends playing a game that they often do while out walking. Each is holding a bag of gold coins, and they bet Heads or Tails on coin flips, such that the winner of the bet keeps the coin that was just flipped. Rosencrantz has been betting only heads and has won 92 flips in a row, as they step onto the stage. They have played this game many times before, and it has always been about even. So, how is this possible? Guildenstern wonders aloud all the conceivable reasons why this would be happening:

Guil: It must be indicative of something, besides the redistribution of wealth. (He muses.) List of possible explanations. One: I'm willing it. Inside where nothing shows, I am the essence of a man spinning double headed coins, and betting against himself in a private atonement for an unremembered past. (He spins a coin at Ros.)

Ros: Heads.

Guil: Two: time has stopped dead, and the single experience of one coin being spun once has been repeated ninety times... (He flips a coin, looks at it, tosses it to Ros.) On the whole, doubtful. Three: divine intervention, that is to say, a good turn from above concerning him, cf. children of Israel, or retribution from above concerning me, cf. Lot's wife. Four: a spectacular vindication of the principle that each individual coin spun individually (he spins one) is as likely to come down heads as tails and therefore should cause no surprise each individual time it does.

We live in a universe of infinite possibilities -- and few of those possibilities are more likely than any others. Shortly after this mini-speech, G. goes on to observe: "The scientific approach to the examination of phenomena is a defense against the pure emotion of fear." In this case, phenomena refers to the unlikely number of heads -- the possibility of the improbable -- but there is a more general truth to what he is saying: Random events -- events that happen without any good reason at all -- scare us, as fragile human beings, and scientific or mathematical analysis is our way to face that fear, if not to conquer it. But I digress...

Part 3: Coin Flips
Flipping coins is even simpler than rolling dice, since there are only two possible outcomes. The probability the coin landing on heads is 1:2 and on tails is (surprise!) 1:2. Does this mean that a coin will land on each side 50% of the time?

1. On the first throw, a coin lands on heads. At that point, the coin has landed heads 100% of the time. If we stopped now. That would be our final tally... far off from our prediction of 50% of the time.
2. The second throw is heads again. Still 100%.
3. A third throw lands tails. This now means that we have landed heads 66% of the time (getting closer to 50%!) and on tails 33%.
4. A fourth toss lands heads, so now we have had heads 75% of the time.

Never once during this brief examination did we find that heads or tails had a 50% occurrence. The only way that you could get that result is if the coin could somehow land as both heads and tails (imagine something like the coin landing on its side) each throw. Since, however, the coin must land on either one side or the other (ie it is forced to be entirely in one of the two possible categories and not somehow both), we can think of a probability as our level of confidence that a particular event will happen. I can only ever be 50% confident that the coin will land heads; I can never believe that one side is more likely than the other to land face up.

Where we see to so 50% start to emerge again is not after a few flips, but when the number of coin flips grows larger and larger. Remember that dice rolling website I pointed out earlier? Well, there's a coin flipping page too. Set Results to Historical and take a look.

At this time I'm writing this, there had been 2,412,539,104 coin flips ever done on that page; 1,206,193,471 of them were Heads. That means Tails landed up over 152,000 times more often. (152,000 times that Guildenstern should have been winning!). But, overall, Heads won 49.99% of the time.

As the number of coin flips approaches infinity (which we will talk about later, I'm sure) the percentage of heads approaches 50% (See how close it was after 2 billion flips?). Likewise, with a 6-sided die, as the number of rolls approaches infinity, the number of 3's that you roll approaches 1/6 (which equals 16.67%).

Get it?

Every American Should See This Chart

"Obama and McCain's Tax Proposals," from the Washington Post



Read every word on it (even the small ones), and this chart basically stands for itself. Love it or hate it (which all depends on your point of view), this is what your family's income will look like in 2009.

The only extra piece of information that I would use to contextualize the numbers is that Obama's tax increase on the top 1% of earners in the country comes from eliminating the tax cuts that Bush put into place at the beginning of his first term. This means that the top 1%'s taxes go back to the same levels as in the 1990s (and they get to keep that 10% extra from the meantime).

Bottled Water

The Environmental Working Group (EWG) is a fantastic organization of scientists and sociologists (people who study the behavior of societies) based right here in the East Bay that studies all kinds of issues in people's everyday lives. Their latest study is on BOTTLED WATER. (If you're a Wave Maker, you probably have already drunk at least one bottle today, so this is a study for you to check out!)

The reason why the EWG did this study is because tap water has to be tested by the government at least once per year to see if there are pollutants, but there is nobody like that testing bottled water. The companies that make bottled water claim that they hold themselves to the same government standards, so the EWG decided to see if they were telling the truth.

The results are not great. First, they determined that Walmart and Giant's store brands ("Sam's Choice" and "Acadia," respectively) are essentially tap water. And those were the healthiest of the brands tested. There were all kinds of pollutants in the other brands, including Tylenol and arsenic:

Altogether, the analyses [...] of these 10 brands of bottled water revealed a wide range of pollutants, including not only disinfection byproducts, but also common urban wastewater pollutants like caffeine and pharmaceuticals (Tylenol); heavy metals and minerals including arsenic and radioactive isotopes; fertilizer residue (nitrate and ammonia); and a broad range of other, tentatively identified industrial chemicals used as solvents, plasticizers, viscosity decreasing agents, and propellants.

The EWG did not name the other 8 brands of bottle water for various reasons, including the fact that the level of pollution in each brand can change over time (eg, a company might change its purification system slightly from one month to the next). In case you are wondering, the Walmart and Giant brands were revealed because they were some of the first tests that EWG did, and EWG is planning to bring a lawsuit against Walmart soon.

Now, there may be some of you at home who are wondering why Walmart would have a lawsuit brought against them, if they were just bottling tap water. Well, that's because California has some of the toughest laws in the county about chemical levels in consumer products. (You are probably familiar with the label: “WARNING: This product contains a chemical known to the State of California to cause cancer" -- note that it's only California and not other states!) Apparently, Walmart was bottling their water in Nevada (specifically in Las Vegas), where they allow higher levels of pollution. If Walmart doesn't change their water soon, they are going to have to start putting that Warning label on their water.

What should you, Wave Makers, do? Stop drinking water?

NO! If bottled water is all that's available, then by all means drink it! Water is one of the most basic nutrients for human beings. But instead of just thinking about what's immediately available to you, start planning ahead.

The first thing that you can do is take that empty water bottle that you just drank and fill it with the filtered water from the tap in the kitchen. That way, you get the healthiest water available and you produce less trash!

The second thing that you can do is buy something like a Kleen Kanteen, which is made of stainless steel, to hold your water. Long story short, many plastics have certain kinds of toxins that leech into whatever is inside of them. I wouldn't worry too much if I were you, especially if you're not putting hot liquids (eg hot chocolate) into them, but in both my and EWG's opinion, it's best to be on the safe side.

[Extra: EWG's last major report came out early in the summer, revealing that 4 out of 5 sunscreens "contain chemicals that may pose health hazards or don't adequately protect skin from the sun's damaging rays. Some of the worst offenders are leading brands like Coppertone, Banana Boat, and Neutrogena."]