Systematic overview of why Sir Robert Anderson's calculations in
The Coming Prince (with regards to the the prophecy of Daniel 9)
are in error for subtracting Julian Leap Days from the result.

10/20/99
-Paul C. Smith

This article assumes a working knowledge of the terms Julian Calendar, Gregorian Calendar, JDN, solar day, solar year, revolution and rotation.  For introductory explanations and basic definitions, see:

http://genealogy.org/~scottlee/cal-overview.html,
http://genealogy.org/~scottlee/calconvert.cgi (for calendar conversions),
and
http://www.capecod.net/~pbaum/date/back.htm.

http://www.execulink.com/~idris/calendar7.html provides information pertinent to a preliminary understanding of the difference between solar days and solar years.

Criticisms and objections will be handled, see footnote at bottom of article.


Introductory premise:
A popular and frequently quoted source by amateur Christian apologists in defense
of the validity of messianic prophecy is Sir Robert Anderson of Scottland Yard, from
his book
The Coming Prince.  Anderson finds precision in the fulfillment of Daniel 9:24ff
by finding exactly 173,880 days, or sixty-nine "weeks" ("sevens") of 360-day prophetic
years, between March 14, 445 BC and April 6, AD. 32 in the Julian calendar. 

This article addresses only one problem with this claim of precision: there are not
173,880 days between these two Julian dates; there are 173,883 (including day one).
Anderson found his "solution" by subtracting three days from the result to "correct" for
the fact that there are 3 more leap years counted in the old Julian calendar than what
is required to accurately synchronize with a solar year.  Our modern calendar,
the Gregorian, handles this more accurately by making only every fourth centennial
year a leap year.  It is this adjustment to his result that this article intends to
show the invalidity of.

Anderson's calculations are flawed primarily because calculations of dates and years
only need to accomodate leap year rules in a calendar when one is trying to calculate:

Sir Robert Anderson is not doing either of these -- he is trying to calculate a precise count
of solar days from a span of time given in... solar days.  Converting that count of days into
solar years in order to immediately divide again and allow leap years into the calculation
is a superflous, unnecessary and erroneous step in the process.  The claim of precise (to-the-day)
prophectic success is based upon a prophetic year of 360 solar days of 24 hours.  Therefore,
one may simply count days in any calendar using whatever leap year rule that calendar
happened to implement, accurate or not relative to a solar year.  The only criterion is that
you count days by accurately following the rules of the calendar you are picking the start and
end dates in.  I will grant without argument the legitimacy of the 360-day year, as
well as the accuracy of Anderson's fixing of the starting and ending events as described in
Daniel 9:24ff. 

It is shown axiomatically and confirmed experimentally below that Anderson's calculations
do not accurately count the number of solar days during the timespan he claims to count.

Identity of some terms as used herein:
A Solar Day =
24 hours, defined by an earth's rotation on its own axis
A Solar Year =
365.242199 Solar Days, defined by one earth revolution around the sun.


Proposition 1:
One can accurately count days between two Julian Calendar
Dates using the Julian Calendar alone, without subtracting
from the result for leap years.

Given any calendar (including the Julian, which did not track
solar years accurately), one does not have to subtract any days
from a count between two dates in order to determine how many
solar days (rotations of the earth on its own axis, which is what
calendar days count) elapsed between the two dates.  All you
need to know is the rules of that particular calendar, erroneous
or not, which for the Julian means that a leap-day is added to every
fourth year.

A very simple example of why this is so is provided at:
http://people.ce.mediaone.net/paulsmith68/DeleteDays.html

Proposition 2:
The Julian Day Numbering system (which is NOT the same as Julian
Calendar Dates), or JDN, is merely a sequential count of solar days
starting with November 25, 4714 BC in the Gregorian Calendar.

It is not meaningful to ask how JDNs deal with leap years, or how many leap years
they include.  It is also not meaningful to ask of a JDN whether that number refers
to a Julian date or to a Gregorian date; it will have a corresponding date in both
calendars, although those dates may be different.  Mistakes in understanding on
this often result from the erroneous belief that a date in the Gregorian calendar
will coincide in time with the same date in the Julian calendar.  This is not so; take
for example today (the day I am writing this).  It is October 20, 1999 in the Gregorian
calender.  However, it is October 7 in the Julian calendar.  Nevertheless, the JDN 2451472
refers to today, and that JDN has counterparts in both calendars.

So A Julian Day Number (JDN) represents a single DAY IN TIME, and any given event in
time can only have happened on one JDN, it does not happen on one JDN for the
Julian calendar and then on another JDN for the Gregorian calendar, since doing so
would constitute the event being dated to two different days in time, given the definition
of a JDN.

Proposition 3:
One can accurately count days elapsed between two JDNs
by subracting the lower JDN from the higher, without subtracting
from the result for leap years.

As long as I pick two dates from the same calendar, I
can use the JDN numbers for those two dates to calculate the number
of days between them; no further adjustments for leap years are necessary.

A Julian Day Number (JDN) represents a single DAY IN TIME.
It does not and cannot "include" or "exclude" "leap years" because
there is no "year" in the JDN system.  JDNs are nothing more than a
sequential count of days elapsed since November 25, 4714 BC
in the Gregorian calendar.  JDNs are neither "Julian days" nor
"Gregorian days" nor even "Jewish days."  JDNs are merely
solar days (24 hour cycles) that have elapsed since the assigned
starting date.

When different calendars (such as the Julian and Gregorian) drift from each
other, they will have different dates corresponding to the same JDN.

For instance, as I write this...
it is JDN 2451472,
it is October 20, 1999 in the Gregorian Calendar,
and it is October 7, 1999 in the Julian Calendar.

Thus as long as I pick two dates from the same calendar (for
example, two different Julian Calendar dates, two different
Gregorian dates, or two different Jewish dates) , I can
use the JDN numbers for these two dates to calculate the number
of days between them; it would be erroneous to adjust this
calculation any further to account for leap-year anomalies.

A very simple example of why this is so is provided at:
http://people.ce.mediaone.net/paulsmith68/OneNumberTwoCalendars.html

Proposition 4:
A calendar's accuracy or inaccuracy with respect to solar years does
not affect the number of solar days between two dates in that calendar.

The Julian Calendar's error in calculating leap years would make
it inaccurate only with respect to solar years, which can be defined either
with reference to the earth's revolutions around the sun, or alternately with
reference to the maximum of the earth's axial tilt.  When counting the solar days
(rotations of the earth on its own axis, which correspond directly to calendar dates)
between Julian calendar dates, that calendar's inaccuracy with maintaining
synchronicity with solar years is irrelevant to the math.

Proposition 5:
It follows from 1, 2 and 3 that every calendar will count the same number
of solar days between the same two physical days in time.

If propositions 1, 2 and 3 are true, then every calendar should yield the
same count of dates between two days in time when one determines
the rules of the calendar, and the date that the calendar assigned to the
two physical days in time
(which can be referenced by JDN).  One must not forget
that two calendars can assign differing dates to the same physical day in time;
I will repeat the example:

as I write this...
it is JDN 2451472,

it is October 20, 1999 in the Gregorian Calendar,
and it is October 7, 1999 in the Julian Calendar.

Proposition 6:
We are in possession of Anderson's starting date, ending date,
and the rules of the calendars in question; the result is 173,883,
and it is immutable.

ANDERSON'S START DATE:
JDN:
1558960
Julian Calendar: Mar 14, 445 BC
Gregorian Calendar: Mar 9, 445 BC

ANDERSON'S END DATE:
JDN:
1732842
Julian Calendar: Apr 6, 32 AD
Gregorian Calendar: Apr 4, 32 AD

Since we have established in proposition 2 that using the
JDN system will yield an accurate count, we can simply
subtract 1558960 from 1732842 (and add 1 since we are
including the first day in the number of days elapsed).

Therefore, 1558960 - 1732842 = 173,882, and
173,882 + 1 = 173,883.

Propositions 2, 3 and 4 have shown that no adjustments to
this number are necessary or warranted; to alter the result
according to how many Julian Leap Years did not occur in
either a solar year or in the Gregorian Calendar is to miscount
the actual number of solar days elapsed between the two
physical days in time.

Proposition 7:
We can achieve further experimental confirmation of propositions
5 and 6 by physically counting the dates each calendar includes between
JDN 1558960 and JDN 1732842.  Doing this experiment confirms
that all calendars coincide in counting 173,883 elapsed days for
the timespan in question.

It will be necessary to download a file to view the experimental
confirmation results.  You can obtain this file at:
www.theism.net/public/anderson.zip.  See the readme for output instructions.
The text file it creates (called "anderson.txt" ) is a table consisting of an
enumeration of every Julian Date, Gregorian Date, Jewish Date, and JDN,
for the period in question, with the respective Day of Week listed as well.

An examination of this table will confirm the following:

a) Every date is accurately and sequentially enumerated in the Jewish Calendar*
b) Every date is accurately and sequentially enumerated in the Julian Calendar
c) Every date is accurately and sequentially enumerated in the Gregorian Calendar
d) Every date is accurately and sequentially enumerated in the JDN System
e) Each line of the table has correct associations between the corresponding Julian Date,
    Gregorian Date, Jewish Date and JDN.
    [f through i: Including the first enumerated day...]
f)  ...there are 173,883 enumerated dates in the Jewish Calendar
g) ...there are 173,883 enumerated dates in the Julian  Calendar
h) ...there are 173,883 enumerated dates in the Gregorian Calendar
i)  ...there are 173,883 enumerated dates in the JDN System

Since a) through i) are true, propositions 5 & 6 are experimentally confirmed.

*Jewish dates were often observationally set, rather than following a strict
algorithm.  Therefore, no calculations in this article are based on the Jewish
dates due to probable inaccuracies with them.

Proposition 8:
We can achieve even more experimental confirmation of propositions
5 and 6 by physically counting the LEAP dates and NON LEAP DATES
each calendar includes between JDN 1558960 and JDN 1732842.
Doing this experiment confirms that the "extra" leap days in the Julian
Calendar for the period are offset by an absence of an equal number of
non-leap days; thus, any further adjustment to the result is superflous.

(This also refers to computations performed on the above mentioned file;
computations were performed in Microsoft Access. 
Click here for instructions
on how to do this yourself.)

An examination of this table will confirm the following for the period between:

ANDERSON'S START DATE:
JDN:
1558960
Julian Calendar: Mar 14, 445 BC
Gregorian Calendar: Mar 9, 445 BC

...AND ANDERSON'S END DATE:
JDN:
1732842
Julian Calendar: Apr 6, 32 AD
Gregorian Calendar: Apr 4, 32 AD

There are 119 LEAP DAYS in the Julian calendar
    for the period between Julian March 14, 445 BC and Julian April 6, 32 AD.
There are 173,764 NON-LEAP DAYS in the Julian calendar
    for the period between Julian March 14, 445 BC and Julian April 6, 32 AD.
119 + 173,764 = 173,883

There are 116 LEAP DAYS in the Gregorian calendar
    for the period between Gregorian March 9, 445 BC and Gregorian April 4, 32 AD.
There are 173,767 NON-LEAP DAYS in the Gregorian calendar
    for the period between Gregorian March 9, 445 BC and Gregorian April 4, 32 AD.
173,767 + 116 = 173,883

Thus it is further experimentally confirmed that the leap year differences
between the inaccurate Julian calendar and the more-accurate Gregorian
calendar cancel each other out.  We can see that there are an identical
number of calendar days between the two physical days in time in both
calendars, and that this number is in fact 173,883.  Thus two seperate
methods confirm propositions 5 & 6, and thus the final result.

Conclusion:
Sir Anderson erred by subtracting three days from his result to account
for the three Julian Leap years that do not occur in the Gregorian calendar
and mis-track the solar year.  The prophetic success of his calculations was
never based on solar years in the first place, but rather on 360-day "prophetic"
years which he finds Biblical support for.  Thus, we must count solar days
and divide by 360 rather than counting solar or axial years.   The sixty-nine
"sevens" of Daniel 9 is reasonably interpreted to mean some sort of seven-year
period, so 69 x 7 x 360 of Anderson's years would be 173,880 days.

The legitimacy of the 360-day year can be granted without argument.
The problem is that in using a year consisting of 360 solar days, it becomes
irrelevant whether or not the calendar used to count the days accurately
maintains synchronicity with the solar or axial year; these calendars could
miscalculate solar years by 11 months, and yet we could accurately
count the number of solar days between two calendar dates without
having to account for anything related to the duration of a solar or axial year.

The unfortunate result of this is that Anderson's oft-quoted calculations which
find precision in the fulfillment of Daniel 9:24ff are erroneous.  Thinking Christians
should analyze this data very carefully -- we have a responsibility to think soberly
before offering anectodal confirmation of our faith which we do not know is true.
Christians should be among the first to eschew dogmatic obstinacy and welcome
honest analysis.

This article remains open to criticism.  I do not expect such a popular document
as Anderson's work to be discarded flippantly; however, I am extremely
confident that the above analysis leaves no room for other conclusions.  It should
also be noted that even without this particular finding of error, many Christian
scholars find this research of Anderson's flawed in other ways; thus, acceptance
of Anderson as a reliable source is hardly universal within Evangelical Christendom.
Many well-studied Christians find altogether different scenarios more plausible
for evaluating this prophetic success; I list two web references below (these pose
entirely different scenarios for computing Daniel's "69 weeks"):

from http://www.themoorings.org/apologetics/69weeks/weeks1.html:
[...B]y treating each week of the sixty-nine as seven 360-day years, Sir Robert Anderson calculated that the period of weeks came to a close on April 6, AD 32; Sir Robert Anderson, The Coming Prince, 10th ed. (repr., Grand Rapids, Mich.: Kregel Publications, 1984), 127. [...] Unfortunately, Anderson made several errors. [...H]e guessed that Nisan 1 was March 14 (ibid., 123). Actually, it was April 13[!]; Richard A. Parker and Waldo H. Dubberstein, Babylonian Chronology 626 BC-AD 75 (Providence, RI: Brown University Press, 1956)
[This author goes on to elucidate problems with the crucifixion date as well]

from http://www.sentex.net/~tcc/dan70.html:
[...O]ne cannot assume, "the Jewish year had only 360 days" for interpreting Daniel's 70 Weeks prophecy. The old year ended and a new one began at a new moon, not after so many days had elapsed, as in our calendars. This fact appears to undermine the interpretation of the 70 Weeks of Daniel popularized by Sir Robert Anderson, ingeneous though it may be. 

We must not be obstinate about contending for falsehoods.   I personally have chosen
the Christian faith in part because I feel it is a choice that is rationally justifiable by the
available data.  Many others have done the same.  The world will be far less inclined
to even consider following in our footsteps if we show ourselves to be unteachable
when facts disagree with some favorable assumption.  Friends, it's time we put this
claim to rest and stopped quoting the "to-the-day" precision of Sir Robert Anderson's
calculations as a reason to believe. 

God bless,
Paul C. Smith
October 20, 1999


OBJECTIONS HANDLED:

If anyone has a logical objection to any of the propositions or underlying presuppositions in this article, I welcome the opportunity to address them.  With the exception of duplications, all objections will be published and answered on the objections page for this article.

Please submit objections individually, clearly and concisely to  webmaster@theism.net for consideration.  A clear, cogent refutation of a specific proposition, a demonstration of how a proposition is based upon a false premise, or a demonstration of how I have misunderstood Anderson's calculations are expected with any requests for me to retract this article.  Please submit each objection as a separate message, to assist us in keeping track of what issues have been answered.  I am confident that the reasons for this will be understood and accepted by the reader.

Hit Counter