Where’s George?

I heard about this website Where’s George? that tracks the circulation of US dollar bills and other paper currency for fun. Since I am interested in networks and the flow of information, I decided to check it out.

You register a bill at the Where’s George? website by entering the denomination, series year, serial number, and your ZIP code. If you live outside of the United States, you can still participate by using the website’s list of global codes. Once you register a bill then…you spend it! If you want to increase the chance of having your bill being reported by someone, you can stamp the bill with information encouraging participants to visit the website and help track the bill’s journey.

Any person who receives your bill and decides to participate in tracking it enters the series year, serial number, and his or her local ZIP code on the Where’s George? website. This is known as a hit. Once a bill is registered, Where’s George? reports the time and distance traveled between hits, and any comments from the participants. Most bills do not receive any hits, but many bills receive two or more hits. Bills that are double- and triple-hitters are common, and some bills have 4 or 5 hits. After the participant enters the hit, then they, too, place the bill back into circulation by spending it.

Fans of the Where’s George? website often collect interesting patterns of hits such as getting at least one hit in all 50 states or getting hits on bills from all 12 Federal Reserve Banks. Fans can rank themselves for fun with their George Score. Your George Score is automatically calculated when you enter bills and get hits on Where’s George? The more bills you enter, and more importantly, the more hits you get, the higher your George Score. The George Score is a method of rating fans based on how many bills they have entered and also by how many total hits they have had. The formula is as follows:

100\times \left[{\sqrt  {\ln({{\rm {bills\ entered}}})}}+\ln({{\rm {hits}}}+1)\right]\times [1-({{\rm {days\ of\ inactivity}}}/100)]
However, since this formula is logarithmic it means that the more bills you enter and the more hits you receive, the less your score increases for each entered bill or new hit. Thus, your score does not increase as quickly when you enter a lot of bills. My George Score is 622.58 (for comparison, the top user has a George Score of over 1500). This makes my Where’s George? rank 6059 out of 16849. But my rank in my state is 277 out of 734.

Adventures In Time And Space 6: Royal Observatory At Greenwich

The Prime Meridian near Flamsteed House

The Prime Meridian near Flamsteed House

The Royal Observatory at Greenwich is on a hill in Greenwich Park in London and is the location of the Prime Meridian. The observatory was commissioned in 1675 by King Charles II for the purposes of celestial navigation and cartography. The king appointed John Flamsteed as the first Astronomer Royal to serve as the director of the new observatory.

The Prime Meridian passes through the Greenwich Observatory complex and is marked by a stainless steel strip in the courtyard. In recent times, a green laser also marks the location and shines across the night sky. The Prime Meridian is part of a geographic coordinate system. This coordinate system is useful for making maps because every location on Earth can be identified by its latitude and longitude.

The latitude is an angular measurement ranging from 0° at the Earth’s equator to either +90° at the north pole or −90° at the south pole. Lines of latitude are circles of differing circumferences on the Earth’s surface. The largest circle is called a great circle and it is the equator. Lines of latitude also are called parallels because the circles are parallel to each other. The equator divides the Earth into the Northern Hemisphere and the Southern Hemisphere. On the Earth’s surface, each degree of latitude corresponds to a distance of about 111 kilometers.

The longitude is an angular measurement ranging from 0° at the prime meridian to either +180° eastward or −180° westward. All meridians are halves of great circles which converge at the north and south poles. The prime meridian and its opposite, the 180th meridian at 180° longitude, together form a great circle around the sphere of the Earth and divides it into the Eastern Hemisphere and the Western Hemisphere. Because lines of longitude converge at the poles, each degree of longitude corresponds to a different distance on the Earth’s surface as the latitude changes. At the equator, the distance is about 111 kilometers, but this distance gets smaller until it reaches 0 kilometers at the poles.

For further precision, each degree of latitude and longitude (°) is divided into 60 minutes (‘), each of which is further divided into 60 seconds (”), e.g., San Antonio, Texas is located at 29°25′26″ N and 98° 29′ 37″ W. These coordinates also can be expressed as decimal fractions, e.g., San Antonio is 29.42412 and -98.49363.

Unlike the equator, which is the one great circle perpendicular to the Earth’s axis of rotation, the location of the prime meridian is arbitrary, and can be part of any great circle that runs through both poles. Throughout history, it was common practice to choose a nation’s capital or some other popular location, so different maps had different prime meridians. Finally, it was decided in 1884 to have delegates from 25 nations meet in Washington, DC, for the International Meridian Conference. The delegates voted to adopt Greenwich as the location for the universal Prime Meridian.

Map of the Prime Meridian at the Royal Observatory Greenwich (south is up)

Map of the Prime Meridian at the Royal Observatory Greenwich (south is up)

Once Greenwich was chosen as the universal Prime Meridian, the longitude at any location can be determined by calculating the time difference between that location and Greenwich. Since a day has 24 hours and a circle has 360°, then the sun moves across the sky at a rate of 15° per hour. As a simple example, if a location is six hours behind the time at Greenwich, then that location is near 90° west longitude. Obviously, a chronometer set to Greenwich time and the local time need to be known.

GPS shows 0.00149 degrees (about 5.3 seconds) due to IERS Meridian being about 100 meters eastward

GPS shows 0.00149 degrees (about 5.3 seconds) due to IERS Meridian being about 100 meters eastward

So why doesn’t the Greenwich Prime Meridian show 0° longitude? The reason has to do with the fact that the Earth is not really a perfect sphere and that, until recently, most maps had to shift their lines of latitude and longitude until they matched local surface measurements to some reasonable amount.

It was only until the existence of artificial satellites that maps finally could be adjusted to the center of the Earth’s mass and not to various local surfaces. The current coordinate system, the World Geodetic System, was established in 1984 (WGS 84) and measures global surface locations to within ±1 meter or better. WGS 84 showed that the Greenwich Prime Meridian was actually about 5.3 seconds or about 100 meters west of 0° longitude. The new meridian is known as the International Reference Meridian and is maintained by the International Earth Rotation and Reference Systems Service (IERS). It is the reference meridian of the Global Positioning System (GPS) run by the United States Department of Defense.

The IERS Reference Meridian is about 5.3 seconds (about 100 meters) east of the Greenwich Meridian

The IERS Reference Meridian is about 5.3 seconds (about 100 meters) east of the Greenwich Meridian

Canyon Lake Gorge

We took a day trip to Canyon Lake Gorge in Comal County.

It is a gorge that was formed in 2002 when the Guadalupe River flooded and spilled over the Canyon Lake reservoir dam and carved through the Glen Rose limestone bedrock. The gorge is around 1.6 km long and 15 m deep. It exposes rock strata that are about 100 million years old. Some fossils present are bivalves (Arctica sp.), gastropods (Tylostoma sp.), urchins (Heteraster sp.), and forams (Orbitolina texana). Also present are dinosaur tracks of acrocanthosaurus and its sauropod prey.

A local group formed the Gorge Preservation Society to develop long-term plans in partnership with the Guadalupe-Blanco River Authority and the US Army Corps of Engineers. Public access to the gorge is restricted to guided tours during a three-hour hike along a designated route, so we just looked around and had a lovely picnic in the nearby park.

The photo below was taken in the Guadalupe River basin on Scarbourough. The view is looking west towards the South Access Road and the gorge beyond.
The photo below was taken on the South Access Road. The view is looking west inside the gorge and towards the Canyon Lake reservoir beyond.
The photo below was also taken on the South Access Road looking west inside the gorge. Notice the transformation of the Guadalupe River basin landscape into a steep bedrock limestone canyon. During the 2002 flood, sediment-loaded water moved massive boulders and sculpted the gorge walls into several channels, terraces, pools, waterfalls, and teardrop-shaped islands.
The photo below was taken on the Corps of Engineers Road looking south. The gorge is to the left of the photograph and travels east for about 1.6 km towards the South Access Road. The Canyon Lake reservoir is to the right of the photograph.
The photo below was also taken on the Corps of Engineers Road but looking east into the gorge. It was here where the Guadalupe River floodwaters went over the Canyon Lake reservoir spillway and carved out the gorge.
The photo below was taken on the Corps of Engineers Road looking north towards North Park Road. The Canyon Lake reservoir is to the left and the gorge is behind the viewer.
The photo below was taken on the Corps of Engineers Road looking west towards the South Access Road and the Canyon Lake reservoir dam beyond. North Park Road is on top of the dam. The gorge is to the left of and beyond the photograph.

Adventures In Time And Space 2: Where The Hell Is Matt?

Dancing 2005

Where The Hell Is Matt?

Video game designer Matt Harding created a video called Dancing that shows him dancing at various locations around the world. After making his video from footage that he collected from his travels in 2003 and 2004, Matt posted it for his family and friends on his blog in 2005.

Matt then made a second, extended video in 2006 with sponsorship from Stride gum. The video is also called Dancing, which he uploaded to YouTube as Where The Hell Is Matt? His website for his experiences can be found here. 

Dancing 2006

Where The Hell Is Matt?

In the 2006 version of Dancing, Matt appears in the following locations (the coordinate system is WGS 84). The list is in chronological order:

  1. Salar de Uyuni, Plurinational State of Bolivia (-20.133775, -67.489133)
  2. Petra, Hashemite Kingdom of Jordan (30.32245, 35.451617)
  3. Machu Picchu, Republic of Peru (-13.163333, -72.545556)
  4. Venice, Italian Republic (45.4375, 12.335833)
  5. Tokyo, Japan (35.689506, 139.6917)
  6. Galapagos Islands, Republic of Ecuador (-0.666667, -90.55)
  7. Brisbane, Commonwealth of Australia (-27.467917, 153.027778)
  8. Luang Prabang, Lao People’s Democratic Republic (19.883333, 102.133333)
  9. Bandar Seri Begawan, Nation of Brunei (4.890278, 114.942222)
  10. Area 51, Nevada, United States of America (37.235, -115.811111)
  11. Tikal, Republic of Guatemala (17.222094, -89.623614)
  12. Half Moon Caye, Belize (17.2, -87.533333)
  13. Sossusvlei, Republic of Namibia (-24.733333, 15.366667)
  14. Routeburn Track, New Zealand (-44.726954, 168.170337)
  15. Monument Valley, Arizona, United States of America (36.983333, -110.1)
  16. South Shetland Islands, Antarctica (-62, -58)
  17. Chuuk State, Federated States of Micronesia (7.416667, 151.783333)
  18. London, England, United Kingdom of Great Britain and Northern Ireland (51.504722, -0.1375)
  19. Karl G. Jansky Very Large Array, New Mexico, United States of America (34.078749, -107.618283)
  20. Abu Simbel Temples, Arab Republic of Egypt (22.336944, 31.625556)
  21. Easter Island, Republic of Chile (-27.116667, -109.366667)
  22. Gare TGV Haute-Picardie, French Republic (49.859167, 2.831667)
  23. Ephesus, Republic of Turkey (37.939139, 27.34075)
  24. New York City, New York, United States of America (40.70569, -73.99639)
  25. Mutianyu, People’s Republic of China (40.438017, 116.5619)
  26. Guam, United States of America (13.5, 144.8)
  27. Mokolodi Nature Reserve, Republic of Botswana (-24.743294, 25.798903)
  28. Berlin, Federal Republic of Germany (52.503056, 13.444722)
  29. Sydney, Commonwealth of Australia (-33.8694, 151.2019)
  30. Dubai, United Arab Emirates (25.117222, 55.198333)
  31. Rock Islands, Republic of Palau (7.161111, 134.376111)
  32. Mulindi, Republic of Rwanda (-1.476389, 30.040278)
  33. Neko Harbor, Antarctica (-64.833333, -62.55)
  34. Kjeragbolten, Kingdom of Norway (59.033564, 6.569722)
  35. San Francisco, California, United States of America (37.819722, -122.478611)
  36. Seattle, Washington, United States of America (47.650955, -122.34728)

Incidentally, the background music is Sweet Lullaby by Deep Forest. The song contains vocal samples from the traditional lullaby Rorogwela sung in the Baegu language. The vocal samples were recorded by ethnomusicologist Hugo Zemp while he was in the Solomon Islands.

Where The Hell Is Matt? Dancing (2005)

Where The Hell Is Matt? Dancing (2006)

Adventures In Time And Space 1: Powers Of Ten

Powers of Ten (1977)

Powers of Ten (1977)

One of the things that makes science so awesome is knowing that all of the wonders of the universe exist all around us but we can notice only a small part of it. We humans are trapped in both time and space by the limitations of our senses. We go about our daily lives using measurement scales that range (in time) from about a second to about a year and (in space) from about a millimeter to about a kilometer.

But events in the universe occur at much smaller and at much larger measurement scales than within these normal human ranges. Science has had to establish a common framework in order to make sense of a far more detailed universe. We use a scale of numbers with a fixed ratio called an order of magnitude.

To make it easy on us, we express the orders of magnitude in factors of ten, i.e., ten multiplied by itself a certain number of times. Each order of magnitude is either ten times larger or ten times smaller than the one next to it, e.g., if a number differs from another number by one order of magnitude, then it is ten times different than the other number; if they differ by two orders of magnitude, then the numbers differ by a factor of 100.

We can use scientific notation to show the order of magnitude in an easy way. If the order of magnitude of a number, say, 2300 is three, then we can express this as 2.3 x 103. If the number was 23000 instead, then it would be 2.3 x 104 and have an order of magnitude of four.

Why bother? Because doing it this way helps us handle very large and very small numbers and gives us a way to compare the scale of things.

The designers Charles and Ray Eames wanted to show this relative scale of the universe. They made a film using the orders of magnitude in factors of ten. They started with humans (naturally) and zoomed outwards from Earth towards the edge of the observable universe. They then zoomed inward towards a single atom and the quarks inside it. In 1977, their film Powers of Ten: A Film Dealing with the Relative Size of Things in the Universe and the Effect of Adding Another Zero was their awesome result:

Powers of Ten (for length)
The examples given are sizes that are within the range of lengths that exist between each order of magnitude. For example, the sizes of elephants, FM radio waves, and humans fall in descending order between one decameter (ten meters) and one meter.

10−18 attometer (quintillionth of meter)
0.000,000,000,000,000,001 (e.g., quark)

10−15 femtometer (quadrillionth of meter)
0.000,000,000,000,001 (e.g., uranium nucleus, proton, neutron)

10−12 picometer (trillionth of meter)
0.000,000,000,001 (e.g., carbon atom, x-rays, gamma rays)

10−9 nanometer (billionth of meter)
0.000,000,001 (e.g., virus, DNA, visible light)

10−6 micrometer (millionth of meter)
0.000,001 (e.g., human hair, white blood cell, bacterium)

10−3 millimeter (thousandth of meter)
0.001 (e.g., rice grain, ant, sand grain)

10−2 centimeter (hundredth of meter)
0.01 (e.g., hummingbird, chicken egg, penny)

10−1 decimeter (tenth of meter)
0.1 (e.g., baseball bat, basketball, cell phone)

100 meter (one meter)
1 (e.g., elephant, FM radio waves, human)

101 decameter (ten meters)
10 (e.g., football field, blue whale, house)

102 hectometer (hundred meters)
100 (e.g., Eiffel Tower, Boeing 747 airplane)

103 kilometer (thousand meters)
1,000 (e.g., Grand Canyon, AM radio waves)

106 megameter (million meters)
1,000,000 (e.g., Jupiter, Earth, Texas)

109 gigameter (billion meters)
1,000,000,000 (e.g., Deneb, Arcturus, Sun)

1012 terameter (trillion meters)
1,000,000,000,000 (e.g., Stingray Nebula, Kuiper Belt)

1015 petameter (quadrillion meters)
1,000,000,000,000,000 (e.g., Orion Nebula, Oort Cloud)

1018 exameter (quintillion meters)
1,000,000,000,000,000,000 (e.g., Large Magellanic Cloud, Tarantula Nebula, Eagle Nebula)

1021 zettameter (sextillion meters)
1,000,000,000,000,000,000,000 (e.g., Local Group, Milky Way Galaxy)

1024 yottameter (septillion meters)
1,000,000,000,000,000,000,000,000 (e.g., Virgo Supercluster)

1027 zennameter (octillion meters)
1,000,000,000,000,000,000,000,000,000 (e.g., observable universe)

Incidentally, 10100 is the number googol. Mathematician Edward Kasner’s nine-year-old nephew coined the word and Edward mentioned it in his 1940 book Mathematics and the Imagination. Of course, this power of ten was the inspiration for the name of the company Google.

The Powers of Ten film from the Office of Charles and Ray Eames was a landmark film. It even became a 2004 couch gag on the opening sequence of The Simpsons (The Ziff Who Came to Dinner):

If we want to show the relative scale of events and not of sizes, then we can use the powers of ten to get a sense of how long events take. We can show how fast atoms react with each other and then go towards larger and larger time scales until we reach the grand age of the observable universe:

Powers of Ten (for time)
The examples given are events that occur within the range of times that exist between each order of magnitude.
For example, the time between normal human heartbeats takes between one decisecond (tenth of second) and one second.

10−18 attosecond (quintillionth of second)
0.000,000,000,000,000,001  (e.g., transfer of electron between atoms)

10−15 femtosecond (quadrillionth of second)
0.000,000,000,000,001  (e.g., chemical reaction time)

10−12 picosecond (trillionth of second)
0.000,000,000,001  (e.g., lifetime of hydronium ion in water)

10−9 nanosecond (billionth of second)
0.000,000,001  (e.g., light travels 30 centimeters or one foot)

10−6 microsecond (millionth of second)
0.000,001  (e.g., strobe light flash)

10−3 millisecond (thousandth of second)
0.001 (e.g., wing flap of honey bee)

10−2 centisecond (hundredth of second)
0.01 (e.g., camera shutter speed)

10−1 decisecond (tenth of second)
0.1 (e.g., human eye blink)

100 second (one second)
1 (e.g., time between human heartbeats)

101 decasecond (ten seconds)
10 (e.g., )

102 hectosecond (hundred seconds)
100 (e.g., )

103 kilosecond (thousand seconds)
1,000 (e.g., class period, movie, concert, football game)

106 megasecond (million seconds)
1,000,000  (e.g., calendar month, grading cycle)

109 gigasecond (billion seconds)
1,000,000,000  (e.g., human life span)

1012 terasecond (trillion seconds)
1,000,000,000,000 (e.g., complete cycle of the equinoxes)

1015 petasecond (quadrillion seconds)
1,000,000,000,000,000 (e.g., length of geologic period)

1018 exasecond (quintillion seconds)
1,000,000,000,000,000,000 (e.g., age of universe)