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Sir Robert Anderson and Daniel 9

EDITOR'S NOTE:
Reader reaction to this article leads me to believe that I have not made its purpose clear.  This article does not seek to refute the proposition that Daniel 9 is a genuine, predictive, prophecy.  Rather, this analysis merely seeks to evaluate the accuracy of one  popular claim about this passage's fulfillment.  To the end of providing a positive evaluation of the predictive prophecy itself, Steve Hinrichs has graciously allowed me to post a copy of his excellent analysis. 

Sir Robert Anderson's calculations regarding Daniel 9
-Paul 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 Scotland 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 accommodate leap year rules in a calendar when one is trying to calculate:

  •     a precise count of solar years from a span of time given in calendar days
  •     a precise count of calendar days from a time span given in solar years

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 superfluous, unnecessary and erroneous step in the process.  The claim of precise (to-the-day) prophetic 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 time span 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 calendar.  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 subtracting 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 1558960 Julian Calendar: Mar 14, 445 BC Gregorian Calendar: Mar 9, 445 BC 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 1732842 Julian Calendar: Apr 6, 32 AD Gregorian Calendar: Apr 4, 32 AD 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 time span 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 and end dates:

START:

 JDN: 1558960 Julian Calendar: Mar 14, 445 BC Gregorian Calendar: Mar 9, 445 BC

END:

 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 separate 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 anecdotal 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: [...by 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: [...one 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, ingenious 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.