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Thus, the early numeral system followed an addition principle and there was no need for a zero. The early Sumerians used the base 60 for their number system. The reason for the adoption of such a large base is probably a reflection of the various units of measure used for commercial, administration and religious purposes.
These were mostly sexagesimal because they afforded many convenient factors of the unit halves, thirds, quarters, fifths, sixths, tenths, twelfths, fifteenths, twentieths, and sixtieths all expressed as whole numbers of the next lower denomination. The next power of the base 60 1 was expressed as a large version of the units 60 0 symbol.
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This was done by pressing the other end of the stylus at an angle. This end was also blunt but had a larger diameter, so it would produced the shape of a larger bullet. These symbols were repeated until was reached when the symbol used for ten a small circle was impressed inside the large oblong symbol for For the next power of the base 60 2 , a large circle was used that was made by vertically pressing the larger end of the stylus into the clay. As with the symbol for , a small circle was impressed inside the larger circle 3, to multiply it by ten and represent 36, Although the Sumerian system had a sexagesimal base, the symbol for ten the small circle was used as an intermediate symbol between powers of sixty.
This simplified the tallying procedure by grouping by ten the ciphers for the different powers. The resulting number was very easy to understand and used the multiplicative principle. The system actually contained only two symbols in two sizes. The small number of symbols made the system very intuitive and available to the masses but needed a fair number of repetitions.
Thus, to write the numbers up to 59, as many as 14 individual symbols were needed for the individual numbers. The small number of numerical symbols was, to a large extent, controlled by the method of writing numbers using a blunt stylus with a circular section to impress marks on wet clay. In this phase, the first use of symbols with determinative value has been found.
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The language represented was probably Sumerian but that is not certain. Nevertheless, the tablets were written in an archaic pictographic script that can be recognized as a precursor of the Sumerian cuneiform script. The writing system was logographic, where one sign or sign-group was used for each term or concept without adding grammatical elements. The numbers as a rule were still made with the round end of a stylus and are easy to identify. A special bi-sexagesimal notation has also been found 5 where two of the same large bullet signs, but with a less elongated impression, were pointed towards each other to signify The first identifiable use of purely phonetic elements and grammar appeared during this time.
In this stage some signs were used to represent syllables. The language used is clearly Sumerian. Most of the material for this period comes from the Archaic Ur tablets. The same number system as in Jamdet Nasr is used. The script was not yet cuneiform, but the signs are more linear. During this interval, writing became much easier and simpler to use, mostly through a change in writing techniques.
The earlier method of incising to make the curvilinear pictorial symbols was gradually replaced by the technique of making impressions of short, straight lines by holding a stylus of triangular section at an angle. Writing now became much faster. The same symbols were used, but many had their form completely changed because the new method only allowed short straight lines.
Superfluous details were omitted, and curved lines were replaced by short straight segments. The short strokes had a head, which was more deeply impressed and therefore wider. Many earlier complicated symbols disappeared. Nissen 7 speculates that the changes in the technique of writing may have had their basis in the increased demand for scribes in an expanding economy. From about BC onwards, the cuneiform script was also used to write Akkadian and Eblaite, which are Semitic languages.
Jubilees and the Knowledge of the Watchers
About eighty percent of the words written on the approximately 10, tablets found at Ebla are in Sumerian. Interspersed are the remaining twenty percent in Eblaite. At that time, the calendar used at Ebla was Semitic and the counting appears to be in Semitic units which were decimal. The number system for representing the counting, however, remained the same as in the previous periods, with the same two different symbols the bullet and the circle and the same two sizes Fig. During the period of the Semitic dynasty of Akkad, the Akkadian language replaced Sumerian as the administrative language, as Sargon I of Agade conquered all of Mesopotamia and extended the empire to the Amanus Mountains to the West, and to the Zagros and Taurus mountains to the East and North.
The wedges of the cuneiform symbols now appear only at the top or the left of the sign. The number symbols, however, could be written in two ways: either as cuneiform signs, inscribed with a stylus of triangular section, or as circular signs made with the blunt end of a circular stylus. The new cuneiform numerals tried to reproduce with wedges the rounded impressions of the earlier numerals.
Thus, an elongated wedge represented the number one and a vertically impressed triangular shape represented the number ten. These symbols were the equivalent of the small bullet and circle of the earlier system. The earlier large circle which stood for 60 2 was now represented by four long wedges making a diamond shape, and the large bullet with the small circle inside 10x60 was written with an elongated wedge and a triangular impression superimposed on its right side Fig.
Similarly, the large circle with the small circle inside 10x60 2 was substituted by a diamond made with four long wedges with a triangular impression inside. Sixty was represented by an elongated wedge which sometimes was larger than the wedge for one, but most of the time had to be differentiated from it by the context or the arrangement of the other numeral symbols.
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This period is marked by the hegemony of the Sumerians under the leadership of Ur-Nammu, founder of the Third Dynasty of Ur, who conquered other Sumerian and Akkadian city-states. As a consequence, there was a revival of the Sumerian language, but only in religious and literary areas, as the language remained unimportant for administrative purposes.
The scribal art reached an exceptional stage of precision.
The round numerals, that had to be made with a different circular stylus, disappeared from current use and only the cuneiform representations, made with the triangular stylus, were employed from now on Fig. A special sign for zero was not necessary. During the Babylonian Period, however, a quasi-positional notation was used that depended on only two signs: the elongated wedge used for the number one and the triangular impression used for The wedge now also stood for the powers of 60 and the triangle for ten times the powers of 60 depending on their position within the sequence of ciphers representing the number Fig.
Eventually, a sign for zero was adopted in the Babylonian system, but it was only used to denote internal empty places, the new numerical symbol was not used to the right of a number as the last symbol. In conclusion, there were two different but related systems for representing numbers in the Sumero-Babylonian culture. An earlier one, based on round impressions using a blunt circular stylus, and a latter one, based on cuneiform impressions made with a stylus of triangular section. The first system appears during the Proto-Sumerian Period and was in use until the time of the Akkadian Dynasty.
Because both systems were sexagesimal and had a limited number of signs, frequent repetitions of the same sign were necessary. An intermediate cipher for 10 was developed to ease the need for repetition and it was used by itself and to multiply the different powers of The individual signs representing a number had to be added together to obtain the actual value of the number.
The earlier system used only two different signs in two different sizes to write the numbers. The cuneiform system also employed only two elements, the wedge and the triangle, but used four wedges to represent the large circle of the earlier system. In both cases, the largest value represented by a single symbol was 36,, although very large numbers could be expressed by the repeated use of the symbol for 36, During the Babylonian Period, however, a quasi-positional notation was developed that allowed for the convenient representation of very large numbers.
Only two signs, the wedge and the triangle, were used to represent the different powers of 60 and 10 times the different powers of 60 depending on the position of the symbol in the number string. A sign for zero was used to indicate internal empty positions. No other culture in the ancient world used the base 60 for their number system. The Egyptians, for example, used a pure decimal notation as well as the Romans and the Greeks.
The Elamites apparently adopted the sexagesimal system from the Sumerians and only used a decimal notation when counting animals. The antediluvian portion of the King List appears to have been originally composed very early in Sumerian history. Therefore, the early number system, based on rounded signs, has been used to represent the numerical part of the list in Fig.
Preservation of Pre-Flood Knowledge
A representation based on the non-positional cuneiform system, however, would have been very similar. The symbols for one, ten, and sixty would not have been needed. Thus, in six of the eight numbers, the durations were given as units of 60 2 , and in the last two with a precision of 10x Notice that all the numbers taken together yield three 10x60 2 signs, thirty-six 60 2 signs, and six 10x60 signs.
To obtain the total of the eight reign durations, the scribe would have used the tallying method. So, for example, he would have counted ten of the large circle signs and written an additional large circle with a small circle inside. In case there were less that ten symbols of the same kind left, they were usually arranged in up to three rows of three symbols each. Thus, the thirty-six 60 2 signs would have yielded three more 10x60 2 signs for a total of six, with six individual 60 2 signs left.
The six large bullets with a small circle inside could have been written as two rows of three signs each, following the convention of the maximum of three rows of three. However, because of the peculiarities of the system, six large bullets with the small circle inside also make a large circle. So, the six 10x60 signs could have been also expressed as an additional 60 2 sign for a total of seven see Fig. The resulting total is equivalent to , years. This number also has a precision of 3, It is curious that the 10x60 signs of the last two durations add up exactly to one of the 60 2 signs, the basic unit of all the other numbers and the overall total, and that the 10x60 unit was not used until the last two reign durations of the list.
A table with the total ages of the antediluvian biblical patriarchs is shown in Fig. The third column is the representation of the ages as decimal-counting Semites would have written them using the early rounded stylus. Exactly what the convention would have been is not known. However, following the same rules for the selection of symbols to represent the different powers of the base as in the sexagesimal system, it would follow that the small bullet and the small circle would represent one and ten, the large circle the next power of the base 10 2 , and the large circle with the small circle inside ten times that power 10 3.
There would have been no use for the large bullet impression because the first power of the base was already represented by the small circle, and no use for the large bullet with the small circle inside because ten times the first power of the base was the square of the base which was represented by the large circle. According to that convention, the total ages of the antediluvian patriarchs would have been expressed as shown in column three.
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The precision of the ages is one year, and the majority of the ages have units. A comparison of Figs. However, if the ages of the Patriarchs are rounded to the two highest digits as in the Sumerian list that appears to be rounded to the two highest sexagesimal ciphers , their representation would be as shown in column 4 of Fig. A total of the eight ages of the patriarchs can also be obtained by tallying all the symbols employed in the individual numbers.
The total would then have six 10 3 signs, six 10 2 signs, and six 10 signs for a sum of years. If we do not incorporate the six 10x60 signs large bullet with small circle inside of the Sumerian total into an additional next higher order sign, the Sumerian total has 6 signs for 10x60 2 , six signs for 60 2 , and six signs for 10x Thus, the totals of both the rounded Genesis and Sumerian lists obtained by a straight tally have six of the signs for ten times the square of the base, six of the signs for the square of the base and six signs for the next lower symbol.
It should be noted that, although the particular form of the symbols used to represent the decimal numbers has been assumed, the relationship of the arithmetic structure of the totals is inherently independent of the symbols used. Nevertheless, the choice of signs employed in Fig. If this was indeed the system used, the resemblance between the totals would have been not only inherently but formally true as well.
A Sumerian scribe looking at a document containing the Genesis total would have interpreted the signs as sexagesimal. The Lord observed the extent of human wickedness on the earth, and he saw that everything they thought or imagined was consistently and totally evil. More on this further down. These human groups have certain distinct genetic differences.
This scientific research is extremely revealing—however, the language comes with a caveat. They are all of a singular species, all humans. According to Dr. So this was not a world of different subhuman species mating. This was simply a world of different human groups intermixing, just as there are clearly different human groups today.
It is identifiable, but certainly no less human. The Bible reveals that God created unique differences in mankind. Adam and Eve would have been highly heterozygous, genetically speaking. Again, by way of example, regarding the popularized Neanderthals: Evidence strongly suggests that they are the Nephilim group of humans named in Genesis This is due to their physique. God designed these humans with a very muscular and stocky build.
The Bible even indicates how they met their demise. As the Bible shows, God had intended for the differences among human groups to be accentuated and highlighted. He intended that groups of like kind stick together, producing offspring among themselves. Again, all human, but all slightly different groups, different families. Yes, with certain differences, but all of the exact same species, all bleeding the same blood.
All descending from a single man and single woman. These all back up the biblical account of how we came to be. That all mankind descended from a single core group and branched out over the Earth, carrying the same customs. But what about the eons-old evolutionary dating? Early cave hand painting, Santa Cruz Province, Argentina. Jesus Christ is the living Head of His true Church.
He speaks to it through new revelation. God has now revealed a physical sign which shows that He has started shaking the nations.