From: Amara Graps (amara@amara.com)
Date: Sun Jul 21 2002 - 10:34:05 MDT
me:
> (I wonder if anyone has calculated the 'mixing factor' of
> countries' Euros with other countries' Euros?)
Some links sent privately to me:
http://www.wiskgenoot.nl/eurodiffusie/engindex.html
http://www.mathe.tu-freiberg.de/math/inst/stoch/Stoyan/e-euro.html
and this article I reformatted:
http://www.wiskgenoot.nl/eurodiffusie/archiefpers/nyt.html
Eurodiffusie: New York Times, 2 juli 2002
Statisticians Count Euros and Find More Than Money
By OTTO POHL
BERLIN When the euro was introduced in 12 countries last Jan. 1,
politicians called it the herald of a new era in European integration
the advent of a common currency that would help break down political and
cultural barriers as well as economic ones.
But for mathematicians, the euro has turned those 12 countries (plus the
three tiny states of the Vatican, Monaco and San Marino) into an almost
ideal laboratory, providing a euros-and-cents way to measure the extent
of European integration and perhaps to understand other phenomena as
well, from the course of epidemics to the movement of stock prices.
While the euro is worth the same in every country that uses it, each one
mints its own euro coins, with a distinctive design on the reverse.
Every time a euro coin from Finland appears in Greece, for example, it
provides a tiny but precise data point about the relationship between
the countries.
So to find out more about their continent, thousands of Europeans are
digging through their pockets and keeping track of their coins, and
mathematicians are tabulating the results in order to figure out just
how fast the coins are spreading.
"This is a historically unique opportunity," said Dr. Dietrich Stoyan, a
statistics professor at the University of Freiberg in Germany, who is in
charge of one of the coin-counting projects. But the goal is not just to
learn more about Europe. "I hope that studying this process will help
people studying epidemics," Dr. Stoyan said. What makes this special is
that the precise launching date of the coins is known. "We know when
this `epidemic' broke out," he noted.
Moreover, the total amount minted was roughly proportional to each
country's economy compared with the overall European economy. Germany,
an economic powerhouse, minted 32.6 percent of all coins, France about
15 percent, and tiny Luxembourg (which used the face of its Grand Duke
Henri) just two-tenths of 1 percent. (All of the euro notes look the
same.) Each country introduced its own coins exclusively within its
borders.
On New Year's Day, the coins, all of them valid across the entire euro
zone, began to spread across national borders. Now, statisticians are
looking forward to the summer travel season, when German tourists can
simply pay for their espresso in Paris with the coins they received in
change that morning at the baker's, back home in Munich.
But how does one model this mingling? Is it simple diffusion, like
opening 12 cans of gas in a giant room and watching the molecules mix?
Or does the relationship between each country depend on a complex set of
equations between each country that considers the distance between the
countries and the number of commuters, travelers and bank trucks going
back and forth?
Dr. Stoyan has gone the complex route. His model is composed of 144
interdependent differential equations that take as many of the known
variables into account as possible, including traveler volume data from
travel bureau associations.
Too many variables, says a group from the University of Amsterdam, which
has chosen simply to take a high-level look at the coin flow. Its model,
based on a branch of probability theory called Markov chains, assumes
that a relatively constant percentage of Dutch coins will leave the
Netherlands each month, and that a different, smaller percentage of
Dutch coins that have already left the country will return. "It's just a
guess," said Misja Nuyens, a doctoral candidate in probability theory at
the University of Amsterdam, who is a member of the group. "We'll see if
we were right, or sadly mistaken."
Each experiment has a Web site for participants to post the contents of
their wallets. Data are tabulated and posted as the experiments go on.
So far, Dr. Stoyan and the Amsterdam group have been surprised to learn
that large-denomination coins for one and two euros move much faster
than smaller ones. Neither knows exactly why that is. Dr. Stoyan
hypothesizes that people tend to dump their small coins out of their
pockets at the end of the day and are therefore less likely to take them
traveling. Mr. Nuyens believes that the coins are used much more often.
And when will the coins reach statistical equilibrium? The models have
yielded different results. The Dutch group believes that half of all
coins in Holland will be of foreign origin a year from now and that
statistical equilibrium across Europe will be reached in five to seven
years.
"I don't think it will go that fast," said Dr. Stoyan, whose
differential equation model predicts it will take several decades.
Dr. Ger Koole, a mathematics professor at the Free University in
Amsterdam who is involved with the Dutch project, hopes the findings
will help expand understanding of applied mathematics.
Phenomena like the "on hold" times at call centers and stock price
movements, he said, are similar to the movements of euro coins: systems
whose development depends largely or entirely on the previous state the
system was in.
For example, to predict the number of calls that will be on hold, you
need to know how many calls were on hold in the previous minute and then
calculate the probability that calls will have been added (new calls
coming in) or have been removed (calls answered or hung up). These
simple calculations, repeated for every time period in question, quickly
can predict the development of complex systems.
Dr. Koole says it is too early to know what will be learned from the
euro experiments. The only way to improve understanding of these
phenomena is "the constant application of theory to see what you end up
with," he said.
The groups agree that the experiment has so many unknowns that it is
difficult to gain scientific clarity, at least at this point. "I have
the distinct impression that a real mania has broken out among coin
collectors," Dr. Stoyan said, which would take rare coins
disproportionately more often out of circulation. In addition, the
self-selected group of participants who log their coins each month is
not necessarily a statistically representative sample.
The best data sources have turned out to be classrooms. The two groups
report that science and math teachers have latched onto the projects as
a way to illustrate their subjects. They either ask all of the students
to examine the change in their pockets or buy rolls of coins at the bank
and count them in class.
Each team has a different model for the effect of the summer travel
season. The Dutch expect that July and August, the two busiest months,
will each count as two or three off-season months. Dr. Stoyan's model
integrates the increased number of travelers. The two teams are hoping
for a spike in interest in the projects, which will get even more coins
counted and improve the results.
Dr. Stoyan, though, is already dreaming of one change that would really
make a difference. "Now if I could just get them to send me the actual
money," Dr. Stoyan said with a laugh.
-- ******************************************************************** Amara Graps, PhD email: amara@amara.com Computational Physics vita: ftp://ftp.amara.com/pub/resume.txt Multiplex Answers URL: http://www.amara.com/ ******************************************************************** "Dare to be naive." -- Buckminster Fuller
This archive was generated by hypermail 2.1.5 : Sat Nov 02 2002 - 09:15:37 MST