As Green As You Think? Consider the Life Cycle

From the New York Times:



The bottom line:

One stainless steel bottle is obviously much worse than one plastic bottle. Producing that 300-gram stainless steel bottle requires seven times as much fossil fuel, releases 14 times more greenhouse gases, demands the extraction of hundreds of times more metal resources and causes hundreds of times more toxic risk to people and ecosystems than making a 32-gram plastic bottle. If you’re planning to take only one drink in your life, buy plastic.
[...]
What it comes down to is this: if your stainless steel bottle takes the place of 50 plastic bottles, the climate is better off, and if it gets used 500 times, it beats plastic in all the environment-impact categories studied in a life cycle assessment.

The God-Einstein-Oppenheimer Dice Puzzle

From Tierney Lab:

"God does not throw dice," Albert Einstein famously declared, but suppose he was wrong. Suppose God decided to demonstrate otherwise by showing up one day at the Institute for Advanced Study. God announces that dice games are in fact wildly popular in heaven, and that the purpose of this visit it to teach a new game to Einstein and J. Robert Oppenheimer. God explains the rules:

There are three blank dice. First, Oppenheimer will take each of the six-sided dice and write the numbers from 1 to 18, in any order he likes, on the 18 faces of the three dice. Einstein will then examine the dice and select one of them as his own. Oppenheimer will then examine the remaining two dice and select one of them. (The third die will be discarded.) Oppenheimer and Einstein will then play repeated rounds of “Dice War” in which they roll the dice simultaneously, with a point being awarded each round to the player who rolls the higher number. The player with the most points wins.

Assume that Oppenheimer and Einstein employ the smartest possible strategies, and that the outcome will be determined by the laws of probability (meaning that God doesn’t skew the dice or the influence the rolls). Which player, if either, is favored to win?

For extra credit, imagine the conversation before, during or after the game.

If you want to test out your theory on who will win and how, here's a handy Dice War simulator.

The Perfect Sunset

Recently, I showed a student of mine a Flash applet from the Astronomy Department at the University of Nebraska-Lincoln. It very generally demonstrates how the sunset changes its North-South location on the horizon during the course of the year (due largely to the tilt in the Earth's axis).

In talking about the sunset's movement, my student expressed to me a lifelong desire: to see the sun setting over the Golden Gate Bridge. It takes a little figuring out, since not only does the sunset move during the year but where it happens depends on where on Earth you are (eg If you are far North of the Equator during the summer, then sunset will appear to happen much farther North than if you were standing at the Equator)!

After thinking about different locations in the East Bay to view the Golden Gate Bridge from, I've determined that Cesar Chavez Park is the optimal place (or possibly the nearby Berkeley Pier).


Latitude is a measure of how far North or South a place on the Earth is from the Equator, so knowing the latitudes of both Cesar Chavez Park and the Golden Gate Bridge will help us to find the date of our particular sunset. Latitude is given in degrees, like the way you measured angles in Geometry.

The Flash applet below gives you control over the Time of Day, Date, and Latitude of the observer. Given that

Latitude of Chavez Park: 37.87^oN
Latitude of Golden Gate Bridge: 37.82^oN

can you use the Flash applet below to find the date of the perfect sunset?

[There are some hints below the applet that may help you.]



Key (for 3-D Observation Simulator)

• Yellow Line: Sun's Declination (Daily Path)
• White Line: Sun's Ecliptic (Annual Path)
• Blue Line (E-W): Celestial Equator
• Blue Line (N-S): Prime Hour Circle

Hint 1

If you're feeling stuck, play around with the Date and Latitude. See what happens in different places at different times of year. What patterns can you find?

Hint 2

Pay close attention to the Sun's Declination. Go ahead and read about it on Wikipedia. There's a continuous measure of declination in the box in the lower left of the applet.

Hint 3

The latitudes of Cesar Chavez Park and the Golden Gate Bridge are just 0.05^o apart. How significant is that in our calculations, considering that our accuracy is limited by that of the applet?

Falling Into a Black Hole

So if you've ever wondered what it might look like to fall into a Black Hole, wonder no longer! From an article at New Scientist, researchers at the University of Colorado - Boulder

built a computer code based on the equations of Einstein's general theory of relativity, which describes gravity as a distortion of space and time.

They follow the fate of an imaginary observer on an orbit that swoops down into a giant black hole weighing 5 million times the mass of the sun, about the same size as the hole in the centre of our galaxy.

[Note: There are more details on what exactly is happening in the video in the article linked above.]


Thanks to Mr. Jue over at the fledgling STEMpowerment blog for the article.