Letters to the Editor

Regarding “Mathematics and
Historical Chronology”
Letters in the August 2013 issue of
Notices regarding Florin Diacu’s article [“Mathematical methods in the
study of historical chronology”, April
2013] dealt mostly with the opinions
of Fomenko and his coworkers. But
there are grave problems with the
content of the article itself. “Mathematical methods” are emphasized
in the title of the article, but Diacu’s
account of them resists my attempt
to understand it.
Consider the account, beginning
on page 443, of the moon’s elongation and its acceleration. What is
meant by “acceleration”? It is clear,
even to a reader who has not specialized in astronomy, that a detailed account of the moon’s elongation must
be complex. One might start from a
naive model of the solar system, in
which the earth moves uniformly in a
circle around the sun, and the moon
likewise around the earth, and moreover these circles are coplanar. In this
model, the elongation increases at a
uniform rate, and its acceleration is
0. To a better, Keplerian, approximation, the orbits are ellipses, the motions of the sun, earth, and moon are
nonuniform, and the moon’s orbit is
inclined relative to the earth’s. All of
these considerations impose periodic
variations on the observed elongation. A yet better model must include changes in the orbital elements
caused by gravitational interactions.
In this complicated context, what
is the meaning of the expression
D  in Diacu’s article? I can only conjecture that after all the accountable
variations are accounted for, there
are long-term changes (on a scale of
several hundred years) that remain.
But I cannot decipher what they are
or what they might mean for chronology.
Another difficulty appears on page
445: “… the 532-year periodicity
of the Easter dates. The last cycle
started in 1941.” What can this mean?
Surely we may mark a beginning
point of any recurring cycle anywhere
we like. We may begin our calen1432

dar year at January 1 or (like many
businesses) at July 1 or (like the ancient Romans) at March 25; it makes
no difference at all to the motion of
the earth.
It would be tedious to go on describing my frustration. In my opinion, the article does not succeed
in communicating what the author
intended.
—Christopher Henrich
chenrich@monmouth.com
mathinteract.com
(Received September 4, 2013)

Response to Henrich
Christopher Henrich first complains
that I do not explain what the acceleration of the moon’s elongation
means. I did not provide more details
because introducing the model would
have taken a lot of space without adding much insight into the chronology
point I was making. Henrich can learn
all the details about this standard
model of celestial mechanics from
the works of Robert Newton and
Anatoli Fomenko mentioned in the
references.
Henrich also writes that cycles
can be started any time, so why did I
mention that the last 532-year cycle
of the Easter dates began in 1941? I
am afraid that he did not read my text
carefully. The point I made in my article is why did the Council of Nicaea
meet in AD 325 but start counting
the first 532-year cycle in AD 345? In
other words, it would have been more
natural to start the count when the
Easter book was canonized, AD 325.
The 1941 start of the latest cycle is a
consequence of this unnatural choice.

With the revelations of Edward
Snowden the public received, and
continues to receive, specific and reliable information about the vast secret spying programs of the NSA that
wildly exceed anything conspiracy
theorists could imagine.
What should be done is a question
not only for U.S. citizens but also for
people all over the world: the NSA
destroyed the security of the Internet
and privacy of communications for
the whole planet. But if any healing is
possible, it would probably start with
making the NSA and its ilk socially
unacceptable­—just as, in the days of
my youth, working for the KGB was
socially unacceptable for many in the
Soviet Union.
The AMS regularly publishes advertisements for positions at the
NSA and manages reviews for the
NSA Mathematical Sciences Grants
Program. The relationship between
the NSA and the AMS seems to be a
symbiotic one: The NSA needs mathematicians for its tasks, and the AMS
has an interest in increasing research
funding. But any relationship with
an organization whose activity is
so harmful for the fabric of human
society is unhealthy. For the sake of
integrity, the AMS should shun all
contacts with the NSA.
—Alexander Beilinson
University of Chicago
sasha@math.uchicago.edu
(Received September 12, 2013)

—Florin Diacu
University of Victoria
diacu@uvic.ca
(Received September 10, 2013)

AMS Should Sever Ties to NSA
I am writing this Letter to the Editor
to suggest the AMS sever all ties with
the NSA (National Security Agency):
Notices

of the

AMS	

Volume 60, Number 11