Onoma
Active Member
OK, now I will bring the " grain " into the conversation ( I have to split this into 2 posts )
Most us already know that the cultivation of grains were central to the fertile crescent (The Cradle of Civilization, as it's also known ), and that in the ancient world it was common to pay workers their daily wages with commodities like beer and bread, etc, and that Barley, or " barleycorn " was one of the staple crops
You may also be familiar with various " grain " measures used in modern times, as a measure of mass ( Mainly )
Grain (unit) - Wikipedia
( I have to add here that this is a case where Wikipedia's weakness and tendency towards dilettante information really shines, as you can see, aside from a mention that the " grain " has been used " since the bronze age ", it basically provides no information or hyperlinks to the other Wiki pages that cover Mesopotamian or Egyptian metrology, all of which discuss, generally, the grain unit and its uses )
But, what isn't generally known is that the barley grain was not just fundamental to society in that it served as sustenance, it also was a fundamental unit of measurement, not just found used for astronomy, but daily life
Another generally unknown type of theme of historical literature are the association between the themes of " farming ", " farmers " and divinity and divine rule ( Sargon of Akkad - " son of a farmer " ), or the associations between divinity / gods and astronomy with farming ( The " plow star " ), which generally dates back to early Sumerian life, when priests also worked in the fields they owned ( The first known corporation, technically, was a group of Sumerian priests that owned the lands they cultivated ), or the various units of measurement in astronomy that also share these themes - the " hand ", the " grain ", the " garden " and so on
The " grain " literally was as fundamental to life in Mesopotamian and Egyptian societies as the foot and the meter are to modern living
As a basic introduction - the following is quoted from Dr. Irv Bromberg, University of Toronto, Canada
Hebrew Calendar Studies: Why Divide Hours into 1080 parts ?
" The duration of a part or " chelek " equals the earlier Mesopotamian barleycorn (pronounced she), the smallest Babylonian time unit, which also represented 1/72 of a time degree ( A unit invoked when we consider earth's rotation )
The time degree was the principal Babylonian unit of time, corresponding to the time required for one degree of motion of Sun across the meridian = 1/360 of a solar day = 1440 minutes per day/360 time degrees per day = 4 minutes per time degree. Thus 4 minutes divided by 72 = 1/18 of a minute = 1 chelek = 1 grain
The time degree also very nearly equals the difference in duration between the solar day and sidereal day, which in the present era amounts to about 3 minutes and 55.9 seconds. The Babylonian finger was 6 barleycorns = 1/12 of a time degree = 1/3 of a minute = 20 seconds of time. The cubit was 180 barleycorns = 5/2 time degrees = 10 minutes of time. The hour itself, corresponding to 15 time degrees.
The Babylonian beru or double hour, corresponded to 30 time degrees. The mean synodic month in Babylonian time units was 29 days, 6 double hours, 11 time degrees, and 1 barleycorn "
( End quote )
Dr. Bromberg's explanation, I feel is sufficient, for the start to this topic, yet he doesn't get into the gradual change in the use of the unit from the time of Naram-Sin, and that change was the shift under Chaldean rule ( Babylonian ), where 1 finger / horn went from being equated to 1° to 1.5° instead, but I'll cover that eventually as we get into the shifts in methods of calculation and the reasoning behind them
As an example, in the Bible, we find this term " chelek " in verses like Genesis 31:14
" And Rachel and Leah answered and said unto him, Is there yet any portion or inheritance for us in our father's house ? "
חלק cheleq - from חלק chalaq - portion, part, flattering , flattery , inheritance , partaker, , share, part, territory , tract, parcel (of land) one's portion, one's possession, (chosen), award (from God) , figuratively - smoothness, seductiveness, flattery
We can see that the use, textually, in the Bible, like many Hebrew terms, is used in different contexts and taken to mean different things, but generally that it's " core " meaning as a " portion " shows its origin to be metrological in nature, and that this metrology would, by logic, would be based on " some " earlier system of units
It is, in fact, not hard to show that Hebrew metrology is taken from earlier systems, but I generally find that this debate is not really necessary ( I'm always open to it, but maybe in a separate thread )
The general definition from the PSD database:
Sumerian : še " barley; grain - a unit of length; a unit of area; a unit of volume; a unit of weight" Akkadian: uţţatu; û; uţţatu
In modern metrology, mathematical physics, etc, we don't think of " time " as some tangible thing, yet under modern theories like the General Theory of Relativity, time itself is established as physical ( Space-time )
In the antiquities, however, " time " was something considered tangible, through the use of the grain unit
It was something you could actually hold, in your hand, with both the " hand " and the " finger " also being units of measurement that were then equated to the period of a pendulum, of a length given in grain
( These graphics are screenshots from the wikipedia page on Mesopotamian metrology, which in this case, is actually rather detailed - but not comprehensive by any means. I have used them simply because they represent the concepts well )
The pendulum has another use though, and that is to establish the nadir - the direction pointing directly below a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface ( The base of the local horizontal coordinate system )
As a pendulum ( Swinging ), as a weight ( not moving ). Specifically, the nadir at a given point is the local vertical direction pointing in the direction of the force of gravity at that location
The nadir is the direction opposite to " elat same " ( the zenith ) identified in my last post with the panel on terms 9 In red ) found used in association with reference to the coordinate system " supuk same " ( The firmament )
You may be familiar with the more modern pendulum equation and the use of the meter pendulum to define the second
A “ seconds pendulum ” is about 1 meter long ( Generally since the force of gravity is slightly different depending on where it's measured on earth's surface, the length of the pendulum associated with the second has varied slightly over time, as various scientists have discovered )
Now as it turns out, there are actually two separate ways in which the ancients calculated time ( This will hopefully lead us into some future discussions on whether or not they solely used sexigesimal ( base 60 ) for mathematics found associated with anything sacerdotal ( Priestly ), because I do not find this to be the case, but I intend to discuss why there's an obvious lack of base 10 mathematics in the literature of a society seemingly based on mathematical knowledge ( Remind me if I forget, this ties into why axioms wouldn't have been directly written down in plain form like what you find with the Greeks )
So, time..
1. Using intervals determined by the period of the pendulum, which gives a nominal day of 86,400 seconds
2. Using intervals determined by the movement of the heavens which gives us 25,920 " parts "
The 2nd one, is what we will find generally used in intercalating calendars, and it is here we will find that the modern Hebrew month interval used, is equivalent to the ancient month length, as both given by Greek as well as Mesopotamian astronomers
25a of the Talmud Bavli tractate Rosh HaShanah states " Thus have I received a tradition from the house of my father's father: the rebirth of the Moon ( This is a New moon - a flood ) is not less than twenty-nine and half days, two-thirds of an hour, and seventy-three parts from the previous one "
29 + 1/2 + 40/(24 × 60) + 73/(1080 × 24) days
= 29 + 1/2 + 40/1440 + 73/25920 days
= 29 + 13753/25920 days
Expressed in base 10 numerals in terms of days with an exact fractional remainder that equals:
29 + 31/60 + 50/(60 × 60) + 8/(60 × 60 × 60) + 20/(60 × 60 × 60 × 60) days
= 29 + 31/60 + 50/3600 + 8/216000 + 20/12960000 days
= 29 + 13753/25920 days
In Mesopotamian base 60, the mean synodic month = 29 days 31' 50'' 8''' 20''''
The decimal representation of the exact value of the traditional molad interval = 29.530594135802469 days
For Judaism, we have
1 day = 25,920 chelekim ( Plural of chelek )
1 Month = 29 + 13753/25920 days
For Mesopotamians, you find that the nominal length of time of a full precession of the equinoxes ( What is associated with astrology ), is 25,920 " years "
I find that this term 25,920 is often attributed to Plato, ( As well as the precession ) however, Plato spent 13 years studying mathematics and astronomy under the Horite ( Egyptian ) priest Sechnuphis. Horites, interestingly are said to be inter-married with the family of Esau, grandson of Abraham through Isaac (Genesis 25:21-25). They were eventually brought under the rule of the descendants of Esau, also then known as Edom - red ) which coincidentally is the color associated with " sacred " mathematics in Egyptian texts ( The Rhind for example ) as well as the color of text considered to be " acts of creation " when read aloud from literature dealing with " magic "
But, that said, 25,920 pops up because it's the more convenient way to synchronize several different calendars
Where we have the luni-solar calendar synchronizing lunar and solar calendars with the use of the synodic month average of 29.53... days ( Intercalation ), we have the ability to synchronize the luni-solar calendar to the movements of the heavens as well ( Precession of the equinoxes )
This allowed accurate prediction of not just eclipses and new moons, but it allowed them to predict where in the mazzaroth / zodiac those events would actually occur ( Along with various other syzygies, etc )
Another little understandably confusing complexity of Mesopotamian phrasing, is that you have identical terms used to refer to different things, and this is common in the literature dealing with astronomy
A " day " or a " month " or a " year " could be referring to time as a terrestrial ( earth ) day/month/year, or it could be referring to them as intervals in the stellar calendars
( Continued in the next post )
Most us already know that the cultivation of grains were central to the fertile crescent (The Cradle of Civilization, as it's also known ), and that in the ancient world it was common to pay workers their daily wages with commodities like beer and bread, etc, and that Barley, or " barleycorn " was one of the staple crops
You may also be familiar with various " grain " measures used in modern times, as a measure of mass ( Mainly )
Grain (unit) - Wikipedia
( I have to add here that this is a case where Wikipedia's weakness and tendency towards dilettante information really shines, as you can see, aside from a mention that the " grain " has been used " since the bronze age ", it basically provides no information or hyperlinks to the other Wiki pages that cover Mesopotamian or Egyptian metrology, all of which discuss, generally, the grain unit and its uses )
But, what isn't generally known is that the barley grain was not just fundamental to society in that it served as sustenance, it also was a fundamental unit of measurement, not just found used for astronomy, but daily life
Another generally unknown type of theme of historical literature are the association between the themes of " farming ", " farmers " and divinity and divine rule ( Sargon of Akkad - " son of a farmer " ), or the associations between divinity / gods and astronomy with farming ( The " plow star " ), which generally dates back to early Sumerian life, when priests also worked in the fields they owned ( The first known corporation, technically, was a group of Sumerian priests that owned the lands they cultivated ), or the various units of measurement in astronomy that also share these themes - the " hand ", the " grain ", the " garden " and so on
The " grain " literally was as fundamental to life in Mesopotamian and Egyptian societies as the foot and the meter are to modern living
As a basic introduction - the following is quoted from Dr. Irv Bromberg, University of Toronto, Canada
Hebrew Calendar Studies: Why Divide Hours into 1080 parts ?
" The duration of a part or " chelek " equals the earlier Mesopotamian barleycorn (pronounced she), the smallest Babylonian time unit, which also represented 1/72 of a time degree ( A unit invoked when we consider earth's rotation )
The time degree was the principal Babylonian unit of time, corresponding to the time required for one degree of motion of Sun across the meridian = 1/360 of a solar day = 1440 minutes per day/360 time degrees per day = 4 minutes per time degree. Thus 4 minutes divided by 72 = 1/18 of a minute = 1 chelek = 1 grain
The time degree also very nearly equals the difference in duration between the solar day and sidereal day, which in the present era amounts to about 3 minutes and 55.9 seconds. The Babylonian finger was 6 barleycorns = 1/12 of a time degree = 1/3 of a minute = 20 seconds of time. The cubit was 180 barleycorns = 5/2 time degrees = 10 minutes of time. The hour itself, corresponding to 15 time degrees.
The Babylonian beru or double hour, corresponded to 30 time degrees. The mean synodic month in Babylonian time units was 29 days, 6 double hours, 11 time degrees, and 1 barleycorn "
( End quote )
Dr. Bromberg's explanation, I feel is sufficient, for the start to this topic, yet he doesn't get into the gradual change in the use of the unit from the time of Naram-Sin, and that change was the shift under Chaldean rule ( Babylonian ), where 1 finger / horn went from being equated to 1° to 1.5° instead, but I'll cover that eventually as we get into the shifts in methods of calculation and the reasoning behind them
As an example, in the Bible, we find this term " chelek " in verses like Genesis 31:14
" And Rachel and Leah answered and said unto him, Is there yet any portion or inheritance for us in our father's house ? "
חלק cheleq - from חלק chalaq - portion, part, flattering , flattery , inheritance , partaker, , share, part, territory , tract, parcel (of land) one's portion, one's possession, (chosen), award (from God) , figuratively - smoothness, seductiveness, flattery
We can see that the use, textually, in the Bible, like many Hebrew terms, is used in different contexts and taken to mean different things, but generally that it's " core " meaning as a " portion " shows its origin to be metrological in nature, and that this metrology would, by logic, would be based on " some " earlier system of units
It is, in fact, not hard to show that Hebrew metrology is taken from earlier systems, but I generally find that this debate is not really necessary ( I'm always open to it, but maybe in a separate thread )
The general definition from the PSD database:
Sumerian : še " barley; grain - a unit of length; a unit of area; a unit of volume; a unit of weight" Akkadian: uţţatu; û; uţţatu
In modern metrology, mathematical physics, etc, we don't think of " time " as some tangible thing, yet under modern theories like the General Theory of Relativity, time itself is established as physical ( Space-time )
In the antiquities, however, " time " was something considered tangible, through the use of the grain unit
It was something you could actually hold, in your hand, with both the " hand " and the " finger " also being units of measurement that were then equated to the period of a pendulum, of a length given in grain
( These graphics are screenshots from the wikipedia page on Mesopotamian metrology, which in this case, is actually rather detailed - but not comprehensive by any means. I have used them simply because they represent the concepts well )
The pendulum has another use though, and that is to establish the nadir - the direction pointing directly below a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface ( The base of the local horizontal coordinate system )
As a pendulum ( Swinging ), as a weight ( not moving ). Specifically, the nadir at a given point is the local vertical direction pointing in the direction of the force of gravity at that location
The nadir is the direction opposite to " elat same " ( the zenith ) identified in my last post with the panel on terms 9 In red ) found used in association with reference to the coordinate system " supuk same " ( The firmament )
You may be familiar with the more modern pendulum equation and the use of the meter pendulum to define the second
A “ seconds pendulum ” is about 1 meter long ( Generally since the force of gravity is slightly different depending on where it's measured on earth's surface, the length of the pendulum associated with the second has varied slightly over time, as various scientists have discovered )
Now as it turns out, there are actually two separate ways in which the ancients calculated time ( This will hopefully lead us into some future discussions on whether or not they solely used sexigesimal ( base 60 ) for mathematics found associated with anything sacerdotal ( Priestly ), because I do not find this to be the case, but I intend to discuss why there's an obvious lack of base 10 mathematics in the literature of a society seemingly based on mathematical knowledge ( Remind me if I forget, this ties into why axioms wouldn't have been directly written down in plain form like what you find with the Greeks )
So, time..
1. Using intervals determined by the period of the pendulum, which gives a nominal day of 86,400 seconds
2. Using intervals determined by the movement of the heavens which gives us 25,920 " parts "
The 2nd one, is what we will find generally used in intercalating calendars, and it is here we will find that the modern Hebrew month interval used, is equivalent to the ancient month length, as both given by Greek as well as Mesopotamian astronomers
25a of the Talmud Bavli tractate Rosh HaShanah states " Thus have I received a tradition from the house of my father's father: the rebirth of the Moon ( This is a New moon - a flood ) is not less than twenty-nine and half days, two-thirds of an hour, and seventy-three parts from the previous one "
29 + 1/2 + 40/(24 × 60) + 73/(1080 × 24) days
= 29 + 1/2 + 40/1440 + 73/25920 days
= 29 + 13753/25920 days
Expressed in base 10 numerals in terms of days with an exact fractional remainder that equals:
29 + 31/60 + 50/(60 × 60) + 8/(60 × 60 × 60) + 20/(60 × 60 × 60 × 60) days
= 29 + 31/60 + 50/3600 + 8/216000 + 20/12960000 days
= 29 + 13753/25920 days
In Mesopotamian base 60, the mean synodic month = 29 days 31' 50'' 8''' 20''''
The decimal representation of the exact value of the traditional molad interval = 29.530594135802469 days
For Judaism, we have
1 day = 25,920 chelekim ( Plural of chelek )
1 Month = 29 + 13753/25920 days
For Mesopotamians, you find that the nominal length of time of a full precession of the equinoxes ( What is associated with astrology ), is 25,920 " years "
I find that this term 25,920 is often attributed to Plato, ( As well as the precession ) however, Plato spent 13 years studying mathematics and astronomy under the Horite ( Egyptian ) priest Sechnuphis. Horites, interestingly are said to be inter-married with the family of Esau, grandson of Abraham through Isaac (Genesis 25:21-25). They were eventually brought under the rule of the descendants of Esau, also then known as Edom - red ) which coincidentally is the color associated with " sacred " mathematics in Egyptian texts ( The Rhind for example ) as well as the color of text considered to be " acts of creation " when read aloud from literature dealing with " magic "
But, that said, 25,920 pops up because it's the more convenient way to synchronize several different calendars
Where we have the luni-solar calendar synchronizing lunar and solar calendars with the use of the synodic month average of 29.53... days ( Intercalation ), we have the ability to synchronize the luni-solar calendar to the movements of the heavens as well ( Precession of the equinoxes )
This allowed accurate prediction of not just eclipses and new moons, but it allowed them to predict where in the mazzaroth / zodiac those events would actually occur ( Along with various other syzygies, etc )
Another little understandably confusing complexity of Mesopotamian phrasing, is that you have identical terms used to refer to different things, and this is common in the literature dealing with astronomy
A " day " or a " month " or a " year " could be referring to time as a terrestrial ( earth ) day/month/year, or it could be referring to them as intervals in the stellar calendars
( Continued in the next post )