The Bewilderness

Debate in Progress

The price of houses in Britain, and the future trend there-of, is a frequent talking point.  Rightmove is apparently the dominant website for houses in Britain, and has compiled an index on the price of housing.  This index is frequently reported in the national newspapers, and the BBC.  An example of BBC story is available here

There is another view.  House Price Crash represents that market segment which either take the view that the market is over-bought, or are priced out.  They are casting a sceptical and partisan eye over the composition of the Rightmove price index in  this discussion thread.

The allegations against the Rightmove index are the following:

1. The index appears to ignore misquotes. 

   The index includes some properties are simply priced incorrectly.  The filter is that they ignore properties a certain number of standard deviations from the mean.  One example is property listed at £130 million.  Such a property would move both standard deviation and mean for the month of listing. The HPC forum turns up large numbers of high-prices properties (as well as a number of properties advertised at £0.)

2. Multiple property portfolios appear to be priced as a single property for the index.

   Again, these might be ignored by the standard deviation filter, but would move the parameters for the filter.

3. The index ignores price reductions. 

   This is a somewhat subtle.  What Rightmove does is simply index new listings.  This obviously avoids the awkward subject of price reductions, but is a reasonable way to measure "this month" activity.  However, the allegation is that Rightmove does not even include price reductions during the month of measurement, and would mean (if correct) that their index is a measure of seller optimism rather than market conditions.

This is going to be topical.  HPC is going to be very noisy suggesting that there is vested interest collusion.  And Rightmove is due to IPO in March. 

Watch this space.

43rd Mersenne Prime

Slightly late, but the 43rd Mersenne Prime was discovered in December 2005.

On December 15, 2005, Dr. Curtis Cooper and Dr. Steven Boone, professors at Central Missouri State University, discovered the 43rd Mersenne Prime, 2^30,402,457-1.  The CMSU team is the most prolific contributor to the GIMPS project.  The discovery is the largest known prime number.

The new prime is 9,152,052 digits long.

The EFF's prizes remain to be won.

Through the EFF Cooperative Computing Awards, EFF will confer prizes of:

• $50,000 to the first individual or group who discovers
  a prime number with at least 1,000,000 decimal digits (awarded Apr. 6, 2000)
  
• $100,000 to the first individual or group who discovers
  a prime number with at least 10,000,000 decimal digits
  
• $150,000 to the first individual or group who discovers
  a prime number with at least 100,000,000 decimal digits
  
• $250,000 to the first individual or group who discovers
  a prime number with at least 1,000,000,000 decimal digits

The Mayan Calendar

The mathematical basis of the Mayan Calendar has proved to be far more accurate over the long term. This is due to the two factors:

Because Central America is located between the tropics of Cancer and Capricorn, the area is an ideal place to develop an accurate calendar, Macri points out. Only in these latitudes is it possible to observe precise solar zeniths, or when the sun is at the center of the sky at noon.

By about 200 B.C., people living along the Gulf Coast in Central America developed the Long Count through their observations of the solar zeniths. The count forms the basis of the more extensive Mesoamerican calendar. The Long Count, with its 13 full cycles of 400 years each, accurately extends back to 3114 B.C., which is when the current era was supposed to have begun.

One wonders how far less accurate Stonehenge is. The religion incorporated observation and calculation: a gentle reminder that knowledge has been embedded in faith far longer than in science.

To handle the uneven counting during leap years, the Long Count developers created an elegant mathematical solution, Macri says.

"They saw how leap years shifted over thousands of days," Macri says. "So, to deal with the fractions, they expressed the numbers by multiplying to get a full number, thus allowing for a more accurate calendar over a long period."

In their observations of solar, lunar and planetary movements over time, the Native Americans were able to create complex mathematical tables. To this day, "daykeepers" in the Guatemala highland serve as Mesoamerican calendar priests by continuing to observe the skies and note their observations, Macri says.

Graduate student Grofe has examined the complex tables used to record the counting cycles that the Mayans used to create accurate projections thousands of years into the past and the future.

"Although computers can calculate time now, these people were very capable of observation and empirical science," says Grofe, who also holds biology and anthropology degrees. "Using complex tables, they recorded unbroken counting cycles over thousands of years."

Are We Slowing Down?

The Great Internet Mersenne Prime Research (GIMPS) is a project designed to find and publish ever larger Mersenne Prime Numbers. This can often act as a lagging indicator of the potential computing power available since it  reflects the potential of current technology. The 42nd Mersenne Prime was discovered in February 2005 using a distributed computing system or, in this case, a 2.4GHz Pentium 4 PC.

The number has 7,816,230 digits and is represented as 2^25964951-1. This was ten months after the 41st Mersenne Prime was number crunched and represents another step towards the $100,000  prize set  by the  Electric Frontirer Foundation for the first ten million digit prime.

Will it take ten months for the 43rd to be calculated?