Mathematical Bias and the Biblical Calendar
(Revised 2015)

By: Shawn Richardson

Section 8:


We have briefly touched upon Jewish history and the documented support of an observational method of new moon crescents and barley crops to determine a calendar, which continued as late as the fourth century of the Common Era. It isn't until this timeframe we find evidence that the observation of signs based on Biblical principles were replaced by mathematical principles. The Encyclopaedia Judaica[9] further confirms this by stating:

So we see that the Biblical event and gathering together on the New Moon was eventually discontinued by men nearly four hundred years after the time of Yeshua. Today, most Jews are fully aware of this historical change and the abandonment of eyewitness testimony in favor of consistent mathematic formulas, not just because it's convenient but, because they have been directed to do so by the Rabbinical authorities. In fact, the initial changeover to a mathematical method is believed to be authorized by a member of the original Sanhedrin Court system, which in their eyes gives this mathematical method an overall stamp of approval.

In Jewish history, the Sanhedrin was a group of men consisting of the wisest elders that were believed to be originated from the Levitical Priesthood - the same group of seventy elders described in Numbers 11:16-24. They acted as court judges in interpreting scripture and Biblical law and it is this authoritative system of judges that appear several times within the New Testament that tried the likes of Yeshua Himself, as well as Paul, Steven and others.

As it pertains to a calendar, we read earlier that it was the Sanhedrin that oversaw the testimony of eyewitnesses of the new moon crescent sightings at the time of the second temple. They believed that it was their ultimate responsibility to determine and inform the people of Israel when the new moons were, indeed, sanctified as the start of each month. At the time, many people in the land looked to the Sanhedrin as the official authority on this subject and accepted them to fill the role of the high priest to sound the shofar trumpet blasts at each new moon. It was also this same group of men that would inspect crops searching for evidence of Aviv barley to begin the year (in addition to other man-made requirements they believed needed to be met). Eventually, the Sanhedrin developed a system of messengers that would quickly spread their findings on such matters across the land of Israel and even further as settlers began to disperse outside the Israeli borders. Even the Roman Christians relied upon the information of these messengers prior to the time of Constantine (as we will see later). Although this group of men created additional rules and practices not defined within scripture, many of them were based on the observational methods that we have seen are required within Biblical scripture.

Much of the history of the Sanhedrin has been preserved and has also contributed to several modern-day Jewish traditions. These historical records detail the procedures and methods practiced by the Sanhedrin that included the interrogation of witnesses who claimed to have seen the new moon crescent. The Sanhedrin would use methods in an attempt to determine the validity of a person's testimony, a system that lasted for many generations up to, and including, the time of Yeshua. Much of these documented practices originated in the first centuries following His death as pressures from the Roman government took a toll on the Jewish authority. Although there were various courts and smaller Sanhedrin throughout the land, the primary Sanhedrin court (also referred to as the Great Sanhedrin) was located at the Temple Mount in Jerusalem. The Jewish Encyclopedia explains this traditional role of the Sanhedrin in their New Moon[30] article:

This traditional celebration is further explained:

We see here that when the Sanhedrin confirmed multiple eyewitness accounts given on the 30th day of the month (since the last new moon crescent was consecrated), the day would be declared and changed as being the first day of the current new moon instead - making the previous month a total of 29 days long. Otherwise, if no witnesses came forward, the new month would begin after 30 days were completed. Although this court methodology was ultimately a man-made system, waiting until the morning for eyewitnesses and confirming their validity before finally authorizing the sounding of trumpets to signal the new moon, this crude procedure became the norm for the Sanhedrin and the people of Israel. However, the basic principles were the same as the Biblical principles we read earlier (and they are fully documented within the Mishna [R. H. ii 5-7]) and clearly were based on a method of observing the Biblical signs. It's also very clear that the Sanhedrin examined eyewitness accounts of, specifically, the new moon crescent, and no other phase of the moon. Judaism 101[35] confirms the details of the Sanhedrin customs:

We see here the added description of sending messengers as confirmation of the Sanhedrin's findings at the time the trumpets were blown each month.

The start of the year (the month of Aviv) was also determined by the Sanhedrin. In fact, they're determination of years based on the barley crops were just one of several variables that would be considered before declaring the moon of Aviv. Arthur Spier, the rabbinical calendar authority, also explains further in his book[44]:

We see that it was by the authority of the Sanhedrin that the people would follow of when to insert a 13th leap-month based on several conditions that were deemed necessary to begin the Passover season. Although not all of these conditions are given in Biblical scripture, it certainly shows that their decisions were not based solely on a fixed mathematical formula.

Another piece of evidence that proves observation was used over mathematics within Jewish history is today's tradition of keeping Rosh Hashanah (the Day of Trumpets) for two days instead of one. Due to the Sanhedrin's crude timing of allowing for witnesses to come forward and report their observations to the court, it was possible that the people would be unclear whether the evening of the 29th, prior to the Day of Trumpets, was actually the Rosh Hashanah Festival day or simply the 30th day of the prior new moon crescent. The Day of Trumpets is the only annual Festival commanded by Yehovah to take place on the first day of the New Moon (considered the first of the secular year by Jews today) and is, therefore, intricately tied with the Sanhedrin traditions that were performed every month. Author N.S. Gill explains the origin of this double-observance tradition in an article titled Secular vs. Religious New Year[39]:

Again, we see the support for mass communications that were employed through the use of signal fires to publicize the event to everyone in the land of Israel. However, these signal fires became unreliable when individuals (Samaritans and Boethusaeans) lit false signals to purposely mislead others to keep different days[17]. In addition to a population spreading further outward from Israel, the Sanhedrin commanded the observation of two days for Rosh Hashanah (Day of Trumpets) if they were, otherwise, unaware that the new moon crescent had been spotted. The fact that this double-observance tradition even came into existence supports an observed calendar methodology prior to the calculated Hebrew calendar used today. Additionally, this tradition has continued into modern Jewish practices even though they now rely solely on mathematical calculations. The Wikipedia Encyclopedia[38] confirms that:

This Encyclopedia article continues:

Due to this Sanhedrin rule, many modern Jews who are now considered in exile (outside of Israel - or the Diaspora) continue to observe two days for the beginning of every new month (after the 29th & 30th day) just in case either is found to be the new moon in the Holy Land - this tradition is called Yom Tov Sheni today. However, this tradition of observing two days for the Day of Trumpets (or the New Moon) is strictly man-made. Obviously, we are not instructed to observe two days for the Day of Trumpets in the Bible; however, we do see a Biblical assembly that gathers together at the expected New Moon in order to be in unison and hear the trumpets sound when the new moon crescent appears. We can see, then, that on the Day of Trumpets this same assembly, patiently looking for the sign in the heavens, must be prepared to keep either day holy as the Day of Trumpets rather than requiring it to be observed for two consecutive days.

We saw how this was laid out in the example of David in II Samuel 20 when we discussed Biblical Months. David planned around two evening meals at the time the New Moon gathering was being prepared, which allows either evening meal (either on the 30th or 31st evening from the prior crescent appearance) to be the sacrificial fellowship meal that would be eaten when the next new moon crescent had come. Just as we should always be watchful of current events that may serve as signs of prophetic times, the gathering together of Yehovah's people at the time of the New Moon, especially on the seventh month that is the Day of Trumpets, we need to be looking up to the heavens for Yehovah's ordained signs that perfectly fulfill the purpose this day pictures: the return of Yeshua, the Messiah!

The fact that today's Jews keep a calculated calendar but also observe two days for Rosh Hashanah suggests that one of these traditions did not always exist and now conflict on principle. Only a change to a mathematical determination explains such a conflict. Dr. Spier continues to explain in his book that the Sanhedrin also utilized other tools in addition to natural conditions.

The Mishna does describe a possibility that the Sanhedrin may have used mathematical calculations to confirm the testimony of eyewitnesses. In fact, one of these documents explains a specific conflict that occurred between two members of the Sanhedrin where specifically the mathematics of the new moon were argued. But we see that the eyewitness testimonies of new moon crescents were interrogated to confirm their sightings and it was these sightings that served as the basis of their ultimate decision - not the math. Whether the Sanhedrin utilized mathematics in addition to the eyewitness testimonies, it would have only been to distinguish whether a witness was likely telling the truth.

It is a member of the Sanhedrin named Rabbi Hillel II who is first attributed to implementing a Hebrew calendar based solely on calculation in the fourth century (358 C.E.). It wasn't until this time we find that the Sanhedrin changed the calendar system to be based on mathematical principles rather than observation. In the Wikipedia article regarding the Modern Calendar of the Hebrews[20], it is explained:

The fourth century was a very dangerous time to be a Jew - most feared for their lives as Paganism (lead by the so-called Christian Constantine) forced its way onto the scene. The Romans established law prohibiting meetings of the Sanhedrin and it quickly became apparent that the standard practices for determining the calendar were not able to continue. Additionally, the Jews were being pushed out of the Promised Land and their temple in Jerusalem had already been destroyed in 70 CE. It became more and more difficult for the Sanhedrin to proclaim new months and years and to send messengers as was traditionally practiced. The Wikipedia Encyclopedia describes part of the tension put on the Jews at this time to adopt a standardized calculated timetable.

In addition, an increasing number of Christian followers began to look for a change to the early calendar system that was still using the Jewish system of observation that Constantine eventually outlawed. It was during this time period that the Catholic Church was establishing its own doctrine and held the historical First Council of Nicaea in 325 A.D. The calendar was one of several topics that were addressed including the determination of Easter, which was being kept by many Christians in the first month that was still being declared by the Jewish Sanhedrin (by this time, the first month was named Nisan). The Wikipedia article[11] states:

The article continues to explain:

We see here a growing majority of Christians were looking for a predictable, calculated calendar instead of one relying on informants, which the Christians viewed as being disorderly. It also supports that the Sanhedrin did not utilize the Spring Equinox (whether they relied on observation, calculation or both). Emperor Constantine pushed for an accurate calendar based on the mathematical Equinox to pinpoint seasons rather than observing the barley crops and the new moon crescents. It was only a few decades after the Council of Nicaea that Rabbi Hillel II is now attributed to succumbing to mathematically computing a calendar for the Hebrew community. This computation was a mathematical average, likely based on Hillel's experience with the Sanhedrin, of observed seasons. In essence, he created a mathematical timetable of the average lunar cycle lengths that coincided with barley crops.

Hillel did not determine his timetable based on the equinox; rather it is an average of how often to insert a 13th leap-month that spanned a repeating 19-year cycle. This way, primarily because the Sanhedrin were being dissolved and the people of Israel were dispersed throughout the world, the people would not have to rely on a Sanhedrin court system. Instead, they could now predict mathematically when to insert the extra month. It provided the best alternative to an organized community searching for the Biblical signs - especially the barley crops within Israel. However, further evidence shows that Hillel did not continue to create the full Hebrew calendar as it exists today, but was only partially responsible for contributing to the current version. The Wikipedia Encyclopedia[22] further confirms that Hillel II...

The Hebrew Calendar we know today was an evolving process that was not fully established until hundreds of years after Hillel's initial concepts were documented. In fact, the topic of the calendar was recorded as being a hot topic and issue of dispute for hundreds of years after the time of Hillel II. If the Jews, through the Sanhedrin, were already maintaining and relying solely on a calculated calendar that was simply made public by Hillel, the question then becomes: why was it such a disputed topic? The Christians viewed the original method of messengers as being disorderly, but if the debated issue was merely a matter of the communication methods being implemented by the Sanhedrin as being disorderly, why didn't Hillel's public declaration continue to be disputed?

We can determine that it wasn't until hundreds of years later when the mathematical computations of the months within the Hebrew Calendar started to be determined based on the mathematical lunar Molad (an average estimate, albeit imperfect, of the moon's lunar cycle from one conjunction to another), rather than the new moon crescent. Although very accurate for the time, the Molad calculation of the lunar cycle differs very slightly from the mathematical calculations of the conjunction we have today. Because of this variance, we can perform reverse-math to determine when the Molad was first instituted by the Hebrews. Dr. Kelley Ross explains this in his article, The Jewish Calendar[26]

He then concludes:

Additionally, this timeframe would have been historically accurate to the level of mathematics of the time. Many who believe the Molad calculation has been preserved from the time of Moses see this as being miraculous and, consequently, presented to man by God Himself. However, this begs the question it God originally provided it, wouldn't it have been completely accurate, without any amount of error? Yet, it is the cumulation of error over time that provides mathematical evidence of just how old this Calendar system truly is, placing it (at the earliest) in the 9th century C.E. This is a very large contradiction from the belief that the Hebrew Calendar was a part of the Oracles preserved by the Jews in the same manner as the scriptures themselves - far from it! It seems that when Hillel II, in 358 C.E., introduced the intercalary 19-year average cycle, he opened the door to a mathematical bias that would eventually replace all of the Biblically observed signs in favor of pure mathematical results regardless of whether these events coincide with the mathematical formulas.

It is not until the 12th century where a certain Rabbi named Moshe ben Maimon "Rambam" (or Rabbi Maimonides) attributed to the calculated Hebrew calendar's accuracy as compared to the solstice or equinox in his book titled Hilchot Kiddush haChodesh in 1178 A.D.[32]. The same mathematical equinox referenced by Constantine's Christian calendar. It was also in the 12th century where we find documented evidence supporting the majority of Orthodox Jews, under the rabbinical leadership, giving into their mathematical bias and relying solely on a calculated Hebrew calendar. In other words, the Hebrew calendar became favored because the math of the equinox was compared to the math of the average timetables and found to best coincide - using math to confirm the math. Nowhere in scripture do we find the equinox even described, much less measured from for counting days, months or determining seasons. This purely mathematical calendar, first instituted in the 9th century and deemed mathematically accurate in the 12th, was the birth of the current Hebrew Calendar used today.

This history strongly contradicts the concept of a preserved Calendar given within the Oracles. Some Hebrew Calendar supporters, though, will claim that the origin of today's calendar was a highly held secret of the ancient Sanhedrin and that its calculations were established through divine revelation from Yehovah Himself! Daniel 2:20-22[1] is referenced as proof of this theory:

We see here that it truly is Yehovah that is in control of the times and the seasons as it is He that sets the celestial bodies into motion, allows the weather to produce crops and can alter any of these signs at any given time. But does that infer that Yehovah gave secret calculations that then control them? Even though Dr. Spier documented that the Sanhedrin practices utilized astronomical facts within the court process - at best it would have been to confirm the testimony of witnesses declaring their sightings of the new moon crescent. But this would contradict with the theory that they relied purely upon calculation - much less used the Molad or conjunction instead of the crescent. We also know that the equinox was not referenced by the Sanhedrin due to Christians changing to this method in their own calendar determinations for Easter.

Could it be that the Sanhedrin possessed calculations for the celestial movements that have since changed? Scripture actually gives us an example where Yehovah stopped time itself. Unlike our ideas of time stopping in a science fiction story, the Bible describes the feat by halting the tracking of the sun and the moon. Joshua 10:12-14[1] explains:

This example clearly tells us that Yehovah directly manipulated the celestial signs to delay time rather than simply issuing a revised set of mathematical formulas. If Yehovah determined times and seasons through mathematics (either directly or indirectly) then we would see a dire need here for them to be adjusted.

But, the question still remains: why would any such mathematics need to be a secret to begin with? Would He not give this information to all of Israel or, at a minimum, mention to them that the Sanhedrin or other particular individuals would have this information bestowed upon them? If so, then who has them today? If it is the Jews and their Hebrew calendar, why are they no longer a secret? But we find no such example of calculations being administered. It then must be considered why Yehovah would give such detailed instructions for the Count to Pentecost and for the counting of days from specific new moons for all of His other Festivals in the book of Leviticus, yet remain completely silent on the math that would be required to determine the dates they are based upon.

The Wikia Encyclopedia[20] discusses the "secret calculations" theory:

This article continues to explain:

Even math proves that the math used today could not have existed in its current state for more than 1100 years - much less from the time of Moses or even during the time of Yeshua. Not only do we not find scripture to support such a theory, but there is also no evidence in Jewish history either. It also contradicts with the Sanhedrin's documented practice of relying on witnesses in determining the new moon. If the Sanhedrin relied on secret calculations, instead, eyewitness testimony would not have been required, the declaration would not have been delayed to wait for witnesses and the commanded traditions of keeping the Day of Trumpets for two days, instead of one, would have never existed. Certainly the Sanhedrin were fallible men, but it seems highly unlikely that Yehovah would have put full trust in their abilities to maintain His secret calendar calculations and not trust the remainder of Israel to even know they existed. This would also go against the instructions Yehovah gave us to not put our faith in the wisdom of men. But if this were, indeed, the case then Hillel went directly against Yehovah's intentions by making this secret public!

In the earlier scripture referenced above, Daniel was thanking the Creator for granting him the wisdom to interpret the King's dreams, but there is never any indication that the authority of times and seasons and the revealer of deep and secret things was declaring that times and seasons were those deep and secret things. Nor are the Sanhedrin ever mentioned receiving any such revelations. If anything we should know of Yehovah by now is that He reveals all things and does not operate "in secret" with mysterious concepts - that is done by Satan with his mysterious Babylonian religions.

The Sanhedrin practices for declaring the new moon developed into the traditions of the Jewish day Rosh Chodesh - a modern-day holiday that celebrates the event of the New Moon. Wikipedia Encyclopedia[36] describes this day as:

Judaism 101, a website that gives basic understanding for Jewish customs and practices, explains the customary Rosh Chodesh ceremony[35]:

Again, here is confirmation that the Sanhedrin relied upon observation of signs. The Wikipedia[36] continues:

We see that the Sanhedrin traditions parallel what we have learned directly from Biblical scriptures. Today's Jews are fully aware of their own history and that of the Sanhedrin which includes an observational-based calendar. They are aware of the significance in the action of blowing a trumpet when sight of the new moon crescent was confirmed by at least two independent witnesses (a principle of II Corinthians 13:1 and John 8:17). This fact is still recognized in their Rosh Chodesh celebrations. The Modern Hebrew Calendar, however, is comprised of mathematical averages and tables that do not coincide with Biblical practices. It is an independent system created to predict future dates without the need of observing the signs. Even though the Hebrew Calendar is likely the closest mathematical calendar in use today that often coincides with actual observation, it does not allow for any kind of variance within Yehovah's creation. Ultimately, perpetual use of the Hebrew Calendar creates a mathematical bias, regardless of when the physically observed signs appear - which can be different by one or two days and, in the case of averaging the barley harvest, a difference of an entire month! But because of their mathematical bias, and because it is found to be mathematically accurate using the equinox, the Hebrew Calendar is today's chosen method that Orthodox Jews and many Sabbath/Festival keeping groups follow.

Today, a Jewish group claims to be the reestablished Sanhedrin[34] created in preparation for any needed court system in the future should the temple in Jerusalem ever be restored. It is believed by these Jews that should the people wish to return to the original traditions, the method of observing signs would once again be standard practice. They further explain in their article Fixing of the Calendar[7]:

This clearly supports the fact that the current calculated calendar will no longer be adequate for the current Jewish community in the near future without some sort of change. Not a strong argument for mathematics being divinely given by Yehovah Himself. Yet, the Hebrew community views an observational method based on witnesses as not only being an acceptable method by Jewish law, but Biblical!

Now that we are familiar with the Biblical principles of a calendar and the history of how the Hebrew Calendar was established mathematically, let's take a deeper look at just how the current Hebrew Calendar is constructed, why it is drifting, and why it's overall architecture and man-made rules may further contradict what we have learned from scripture.

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