The Unique Digital Table

We all know that a digit is a numeric symbol such as "2" or "5" used in combinations, such as "25" to represent numbers as the number 25 in positional numeral systems. The name "digit" comes from the fact that the 10 digits, Latin "digiti" meaning fingers of the hands, correspond to the 10 symbols of the common base 10 numeral system. In a basic digital system, a numeral is a sequence of digits, which may be of arbitrary length. Each position in the sequence has a place value, and each digit has a value. The value of the numeral is computed by multiplying each digit in the sequence by its place value, and summing the results. As of digital values, each digit in a number system represents an integer. For example, in decimal the digit "1" represents the integer one. So, digits are:

1 2 3 4 5 6 7 8 9


It is a well-known fact that if we add 9 to 9 we still get 9. 9+9=18 (1+8=9), 9+18=27 (2+7=9); But if we do the same with all real numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9, we found that all numbers have an unique order. We started with 1+1=2, if we continue adding 1 to the sum, 1+2=3, 1+3=4, 1+4=5, 1+5=6, 1+6=7, 1+7=8, 1+8=9, 1+9=10 (1+0=1), 1+10=11 (1+1=2), and it continues eternally 1+11=12 (1+2=3). So number 1 has the following order 2 3 4 5 6 7 8 9 1.

We did the same to all real numbers; the table how each number generates its order and the result was the table of fine order of numbers. This table includes the understanding of multiplication table, it draws a beautiful unique image, plays a blissful music and many others that you will discover on this site and may be you will have your own discoveries
.

1

2

3

4

5

6

7

8

9

1+1=2

2+2=4

3+3=6

4+4=8

5+5=10 (1)

6+6=12 (3)

7+7=14 (5)

8+8=16 (7)

9+9=18 (9)

1+2=3

2+4=6

3+6=9

4+8=12 (3)

5+10=15 (6)

6+12=18 (9)

7+14=21 (3)

8+16=24 (6)

9+18=27 (9)

1+3=4

2+6=8

3+9=12 (3)

4+12=16 (7)

5+15=20 (2)

6+18=24 (6)

7+21=28 (1)

8+24=32 (5)

9+27=36 (9)

1+4=5

2+8=10 (1)

 

4+16=20 (2)

5+20=25 (7)

 

7+28=35 (8)

8+32=40 (4)

 

1+5=6

2+10=12 (3)

 

4+20=24 (6)

5+25=30 (3)

 

7+35=42 (6)

8+40=48 (3)

 

1+6=7

2+12=14 (5)

 

4+24=28 (1)

5+30=35 (8)

 

7+42=49 (4)

8+48=56 (2)

 

1+7=8

2+14=16 (7)

 

4+28=32 (5)

5+35=40 (4)

 

7+49=56 (2)

8+56=64 (1)

 

1+8=9

2+16=18 (9)

 

4+32=36 (9)

5+40=45 (9)

 

7+56=63 (9)

8+64=72 (9)

 

1+9=10 (1)

2+18=20 (2)

 

4+36=40 (4)

5+45=50 (5)

 

7+63=70 (7)

8+72=80 (8)

 

2 3 4 5 6 7 8 9 1

4 6 8 1 3 5 7 9 2

6 9 3 6 9 3 6 9 3

8 3 7 2 6 1 5 9 4

1 6 2 7 3 8 4 9 5

3 9 6 3 9 6 3 9 6

5 3 1 8 6 4 2 9 7

7 6 5 4 3 2 1 9 8

9 9 9 9 9 9 9 9 9

 

9 9 9 9 9 9 9 9 9
7 6 5 4 3 2 1 9 8
5 3 1 8 6 4 2 9 7
3 9 6 3 9 6 3 9 6
1 6 2 7 3 8 4 9 5
8 3 7 2 6 1 5 9 4
6 9 3 6 9 3 6 9 3
4 6 8 1 3 5 7 9 2
2 3 4 5 6 7 8 9 1

1. The Multiplication Table

Now let's start looking into it. If you analyze the table in vertical order you will get the multiplication table, because 2X1=2; 2X2=4; 2X3=6; 2X4=8; 2X5=10=1; 2X6=12=3 2X7=14=5; 2X8=16=7; 2X9=18=9. And it is the same with all the rest.

 


 

2. The Infinity

It is endless and demonstrates how we float on the surface of infinite numbers.

 

9 9 9 9 9 9 9 9 9
7 6 5 4 3 2 1 9 8
5 3 1 8 6 4 2 9 7
3 9 6 3 9 6 3 9 6
1 6 2 7 3 8 4 9 5
8 3 7 2 6 1 5 9 4
6 9 3 6 9 3 6 9 3
4 6 8 1 3 5 7 9 2
2 3 4 5 6 7 8 9 1

Now pay attention in the above table to the half boxes on the left 7 5; 1 8; 4 2; and on the right 8 7; 5 4; 9 1. It means if we stick the same table on all four sides of it, it will smoothly connect to it and make an endless table where it always leaves the half boxes to attach more and more infinitely. Let's see:

To visualize better:

And if you cut through repeated 9s, you will get this:

8

7

6

5

4

3

2

1

7

5

3

1

8

6

4

2

6

3

9

6

3

9

6

3

5

1

6

2

7

3

8

4

4

8

3

7

2

6

1

5

3

6

9

3

6

9

3

6

2

4

6

8

1

3

5

7

1

2

3

4

5

6

7

8

Let's call this a table after an infinity cut or infinite table.


3. Unique Orders

If the numbers in the table are replaced with the symbols (in this example the Latin alphabet) the unique arrangement can be seen, after the infinity cut.

 

After transforming into the infinite table, we get this:

 


 

4. The Digital Painting

If the numbers in the table are replaced with colors of standard palette: red, orange, yellow, green, blue, cyane. indigo, indigo ultra and violet; there is certain arrangement of colors. But if the image is being influenced by putting any simple computer filter effect on it the rows of color violet (9) creates 8X8 tables, where a certain geometrical object is created, like an unique digital painting.

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 RED; 2 ORANGE; 3 YELLOW; 4 GREEN; 5 BLUE; 6 CYANE; 7 INDIGO; 8 INDIGO ULTRA; 9 VIOLET

Again, if we transform this into the infinite table we get this:

 

 

In any versions of colors you will get one and the same image with two inversed versions only:


 

5. The Digital Music

If the numbers in the table are replaced with notes of music in the infinite table: do, re, mi, fa, sol, la, si, do, and re; there is a certain arrangement of sounds.

do

si

la

so

fa

mi

re

do

si

so

mi

do

do

la

fa

re

la

mi

re

la

mi

re

la

mi

so

do

la

re

si

mi

do

fa

fa

do

mi

si

re

la

do

so

mi

la

re

mi

la

re

mi

la

re

fa

la

do

do

mi

so

si

do

re

mi

fa

so

la

si

do

If you play this with this direction from bottom to the right like do, re, mi, fa, sol, la, si, do, re, fa, la, do etc. you will get:

Download the MIDI sound file here.

 


 

6. Discover 9 everywhere

If you select the area on The Unique Digital table with 6X6 or 3X3 boxes, whatever sum its numbers are; it will finally equal to 9. Wherever you select.


This observation is first made on 26th of July, 2009 by Giorgi Dolidze. All rights are reserved (2017)

If you have any further discoveries, interest or just a question. Please, contact g.dolidze@isie.ge or call +99 55 99 88 11 06.