In the chapter concerning Revelation. We worked with a numberline of seven places. Let us go back to that line and look at some of the other things it reveals. The first digit and the last digit are the numbers 1 and 7. These two total the sum of 8. The second pair of digits is 2 and 6, which also total 8. 3 and 5 are next, also totaling 8. Since this numberline has an Odd number of digits, as seven is an odd number, there are no more pairs left. The number 4 is left alone in the middle. 4 is half of 8, so the place it has in the center, which is the halfway point, is very appropriate. Take a look at the complete digital numberline below.

    These are the ten digits of the decimal system arranged in order of value. This is the primary line of all that we will work with. This line repeats itself when numbers are reduced to prime digits in reduction, with exception of the zero, as it occurs only once. In this line, the ends are 0 and 9, which total nine. The next pair are 1 and 8, which also total nine. 2 and 7, 3 and 6, and 4 and 5 also total nine. As this line has an Even number of digits, the middle falls between two numbers on the line: in this case, between 4 and 5. Half of nine is also 4.5 in the decimal system, or just 4 and a half plainly.

    This line also demonstrates the division spoken of earlier between the definers and the defined. 1 + 2 + 3 + 4 = 10, which is the nine and the zero. We dropped the zero for the first half of the line, so we must drop the nine in the last half now, as nine is symbolically the equivalent of zero mathematically. The second half of the line is thus 5 + 6 + 7 + 8, which has a sum of 2 x 13, or 26. Again, this distinction between 10 and 26 will be addressed later in this work. This demonstration simply points out another way to reach it logically.

    To enable further study upon the significance of certain numbers, and numbers in general, let us now consider a common table of multiplication used in mathematics. Children use this table all of the time. It is a very simple square table showing the factors and sums of multiplication basics in an X-Y type grid as shown below. For our use though, it will be limited to only eight digits, as any number multiplied by nine equals nine:

    The row across the top is 1 multiplied by each of 8 numbers. The column down the left side is each number multiplied by one. The factors that are normally on the top and side of this sort of table have been left out. The next table is really the same as this one; the difference is that all of the sums have been reduced to single digits.

    There are many things to be noted here. First, there are only four nines present, in a square pattern in the center of the table. Second, the patterns of the second four numbers are the exact opposite of the first four. Third, any two numbers that are the same distance from the center along a horizontal or vertical line add to nine. Fourth, that only the numbers 1,2,4,5,7,and 8 have themselves as sums of their multiplication. The other three numbers; 3,6, and 9 can only result in a 3,6, or nine when multiplied by any other number. His forms a kind of grid between the multiples of three, that looks like a "Tic-tac-toe" grid. A further analysis reveals even more repeating patterns, but let us concentrate upon these for now:

    Ignoring the grid formed by the multiples of 3 and 6 leaves nine smaller squares, each containing four numbers. Each of these squares also adds to nine, (1 + 2 + 2 + 4), (4 + 5 + 8 + 1), etc. Four times nine again adds to thirty-six.

    The numbers 3, 6, and 9 can be thus set apart from the other numbers for now, so that we may look at these other six numbers. 1,2,4,5,7,8 they are in logical order. The sum of these six added is 27. The first three seem to suggest some sort of pattern themselves. 1 + 2 + 4 = 7, but the pattern is more than this. This is a doubling sequence. It is the same pattern which organic cells divide into. One splits into Two. Two split into Four. The logical progression of this is then that Four split into Eight, and Eight into Sixteen, and Sixteen into Thirty-two, and Thirty-two into Sixty-four, and so on. This pattern can also be resolved from these six numbers.

    The 1 2 4 pattern is sequential in the numberline. To get the 8 we have to start from the opposite end. As the multiplication table shows us the cycle of 8 is the opposite of 1, this should come as no surprise. The sixteen that the 8 doubles into is reduced: 1 + 6 = 7, which is the next number in the reverse order we are following. The 16 into 32? 3 + 2 = 5, as does 7 + 7 = 14, which is 1 + 4 = 5. So this entire sequence is here in these six numbers, only it is broken in half and turned around in the middle. The sequence we are discussing is infinitive. This is a cycle of six numbers that repeats over and over again forever. In this work, infinitive numbers, especially fractions and decimals, will be represented by the sign ~ following the number where the sequence repeats. 1 2 4 8 7 5 is the sequence. What does this look like on a numberline?:

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Copyright 2000 by J.S.Graham