Written on April 11, 2004 (4 WE).
1. Introductory notes to numerics and numerical systems
We was looking at the 7th WS file for the pick-3 lottery game. It deals with the low/high and odd/even situations. The total of possibilities is: 23 x 23 = 8 x 8 = 64 (or 26). Well, there is no single-sign expression for the elements beyond 9. The first of the 64 elements may be expressed as 0-0-0-0-0-0, or low-low-low-even-even-even. The last of the 64 elements can be expressed as 1-1-1-1-1-1, or high-high-high-odd-odd-odd. The last element can't be expressed as a single-sign numeric, but only as a two-digit measure (64).
The hexadecimal numerical system can express values above 9 as single-sign symbols by using alphabetical symbols (the letters A to F). But that's not entirely logical. The letters symbolize words, not numbers. Why shouldn't we think of single symbols to accommodate the numerical systems computers work with? Most computers now are considered powerful because they are capable of working with 32 bits of information. But the humans use tricks to quantify data. They put together two hexadecimal numerical values, sometimes consisting of the F word! What number is that?
2. The important role played by numeric systems in the history of civilizations
I wrote earlier (way early!) about the importance of Almighty Number in civilization. ”From the dawn of civilization, the most advanced societies were the most intense number-worshippers. First, the Egyptians. The Egyptian influence passed on to the Greeks. Pythagoras converted the number from religion-only to philosophy (“God is the Number”). Renaissance took one more step and converted the number from philosophy into science. Then on to the highest peak of number worshipping: the United States civilization. The number has become the way of life. Every computing beast is a (social security) number. Now, China is trying to enter the temple of Number. They understand that the number one sin of Communism was “mocking the Number”. That's why Communism collapsed in the first place.”
In truth, the main aspect of this is the number of single symbols used to express numerical values (quantities). The Classical Greeks were brilliant thinkers. One wonders why they didn't achieve a whole lot more technologically. Well, I don't think they had a grasp of numerical expressing. It's hard to understand how they used numbers. They did use the numbers, but their method was cumbersome!
The Romans were brilliant in engineering. They did use the numbers, but their method was also cumbersome! They improved on Greek mathematics, but those X and XI, and XVI were not easy to work with! No wonder they were unable to devise computers!
We all recognize the extraordinary role the Renaissance played in history. I am afraid we do not give deserved credit to the Arabs for making Renaissance possible. For centuries before Renaissance, the Arabs were far more advanced than the Europeans of the Dark Ages. The Arabs took advantage of the brilliance of the Classical Greeks, in a time when the Europeans considered the Classical Greeks as sinners with dangerous ideas! The Arabs also were using a new and very powerful instrument: the 10 digits of the base-10 numerical system. Granted, they took the idea from the Indians of Sanskrit India. The Indians, and then the Arabs used 10 single symbols for the 10 atoms of the 10-base numeric system. That was the revolution the humans do not pay respect to at all! Renaissance would have not been possible without the 10 single symbols for the base-10 numerical system! Mathematics exploded. Human knowledge exploded as a result of the mathematical explosion. We are OK now, the humans. But a new explosion will occur as soon as mathematics explodes again.
3. A new numerical system to keep up with developments in science and technology
What I am presenting here and now does not imply explosion by any stretch of imagination. I only think of devising single symbols to quantify numbers in numerical systems above 10. Humans should keep pace with their own devices. If computers “work” now in the 32-base numerical system, the humans should be able to work naturally with 32-base numbers. The 64-bit computer processors will enter the main stream soon. Can we count in 64-base using single symbols? NOT! We'll need more letters to build on the hexadecimal system! How about the 128-base numeric system? No way we can handle that naturally. But we should be able to, if we create such symbols.
I don't want to blow away the 10 symbols of the decimal numeric system. There is a lot of information stored in that system. Of course, the Greeks and the Romans left behind a lot of information that was not compatible with the 10-base system. Nevertheless, history was able to convert the information and make best use of it—for all intents and purposes! For simplicity, however, let's keep in use the 10 single symbols of the base-10 system that made such a revolutionary contribution to human development. If we need to worship, these gods deserve worship most: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Well, we still have problems comprehending that the first atom is 0, not 1. We take and give 10 as the perfect mark, but 10 is actually element #11 in the 10-based numerical system! We should mark our efforts on a scale from 0 to 9, not 1 to 10! That means consistency!
Ok, so let's keep the 10 traditional numerical symbols. The hexadecimal system adds the letters A, B, C, D, E, and F to create the 16 necessary single symbols for the numerical hexadecimal system. But why letters, I might ask? Letters are for words, not numbers.
I propose the usage of symbols that are more related to mathematics, such as geometrical symbols. Let's replace the 6 letters by geometrical shapes. I would start with the first half of the circle. Slice the circle by the vertical diameter. The left semicircle is the first symbol that comes after the symbol 9. The right semicircle is the 2nd symbol after 9. The triangle is the 3rd symbol. The square (four sides, get it?) would be the 4th element. The pentagon would be the 5th, and the hexagon would be the 6th element after 9. At this point, we cover the hexadecimal system entirely. Instead of the letter F, we can use the hexagon as the 16th element of the hexadecimal numerical system.
We only used single-line, empty geometric symbols. We can add 6 more symbols by putting a dot inside each geometrical shape. We can also draw two horizontal dots inside each shape. We can go further, and add three vertical dots. Four vertical dots can be drawn as a rhomb inside each shape. A maximum of 5 dots can be drawn as a cross inside each shape. Six single-line geometrical shapes with from 0 to 5 dots means a total of 6 x 6 = 36 single symbols for numeric systems. Up to 5 dots makes it fairly easy to comprehend a symbol without further written reference. We want to cover up to 128-base numeric system. We can use multiple-line geometric shapes and also from 0 to 5 dots inside. Up to 5 lines would still make it mnemonically easy to comprehend every symbol without further reference. We would have in our treasure chest a total of 36 x 5 = 180 single symbols to work with numbers in base systems larger than 10. We must keep up with our computers. We must also be able to express better our gratitude to Almighty Number. We can say larger and larger numbers that now we can say as :”googles of googles”.
Most humans don't realise how important the numbers and their symbolization have been throughout our history. If Pythagoras and Archimedes had come up with ten single numerical symbols, humanity would be now like it will be some two thousand years from now. Mars would definitely be populated by humans at this time.
4. Essential (and thoughtful!) resources at Saliu.com
Resources in Theory of Probability, Mathematics, Statistics, Combinatorics, Software.
See a comprehensive directory of the pages and materials on the subject of theory of probability, mathematics, statistics, combinatorics, plus software.
Resources in Philosophy, Humans, Humanities, Ideas, Truth.
See a comprehensive directory of the pages and materials on the subject of philosophy, humans, humanities, ideas, truth, Human_Computing_Beast.