Numerals vs. Alphabets

Having said that, the use of both of the other numbering forms is still widespread, as is the use of Chinese numerals. As an aside it should be noted that even some of the Chinese numerals are related to the Indic and Arabic forms. The complete set is:
一， 二， 三， 四， 五，六，七， 八， 九，〇

For any technology—and here we are considering the numerals to be a technological tool or system—there also has to be a mechanism for it to be shared.

Ah, yes, the abacus — more related to the question of numerals than one might imagine. But let us consider a different technology first:

Consider paper, an amazingly useful and now ubiquitous technology, usable for everything from use in the toilet to printing money, not to mention books. Paper is one of those products that if any reasonably technically minded person sees it being made, even just once, they can quickly figure out how to reproduce the manufacturing process. Paper is at its core a very simple product that can be made with a wide variety of different fibers, it is strong, versatile, lightweight and useful for a myriad of purposes. In other words, amazingly effective. But—here is the big caveat—rather than people wishing to share the technology, each group of people that figured out how to make paper purposely sought to prevent the spread of the secret to making it. Hence it took from roughly 200 CE to between 1085 CE (Toledo, Spain) to 1320 (Mainz in what is now Germany) for papermaking to make its way from China to Europe on what was a well-traveled international throughway for goods and ideas. (History of paper – Wikipedia

Another fantastic idea was the phonetic alphabet system developed by the Phoenicians (the Proto-Canaanite writing system) in c. 1050 BCE.

The Phoenician alphabet is derived from Egyptian hieroglyphs. [5] It became one of the most widely used writing systems, spread by Phoenician merchants across the Mediterranean world, where it evolved and was assimilated by many other cultures. The Paleo-Hebrew alphabet is a local variant of the Phoenician alphabetical script. [6] Another derivative script is the Aramaic alphabet, which was the ancestor of the modern Arabic script. The Modern Hebrew script is a stylistic variant of the Aramaic script. The Greek alphabet (and by extension its descendants, such as Latin, Cyrillic, Runic, and Coptic) was also derived from Phoenician.

Ultimately nearly every phonetic alphabet system in the world derives from Phoenician or its various descendants. (Phoenician alphabet – Wikipedia) The concept of a small set of signs that are able to represent individual sounds was a disarmingly simple but highly effective method of representing language. The system was adapted for one language after another.

The numbering system we call the Hindu-Arabic numeral system is far more recent than alphabetic writing, having been developed by mathematicians in the Indian subcontinent sometime in the 1st to 4th centuries CE. The system itself, like the concept of a phonetic alphabet, is the key, rather than the particular symbols used to represent the numerals. The system which makes the number system so effective is that it is a positional decimal numeral system, including a zero. The history of zero is not as straightforward as one might think, and was independently thought of at various times and places in history. Zero has to be considered as a concept, as a placeholder, and as a numeral (for more see Who Invented Zero?). What is important for this discussion is that the system developed in India not only used zero as a number, but included the concept of a decimal place holding system: that is a base ten number system in which each column represents 10 times the previous. A column for 0–9, a column for each numeral times 10, a column for each numeral times 100, and so on. This system functions wonderfully for doing all sorts of calculations, both by mathematicians and by those who need to calculate on a daily basis for applied purposes.

Rather than trying to keep this number system a secret, Indian mathematicians freely shared their work. The system was adopted by mathematicians in the Islamic world in the 9th century. Highly influential in the spread of the system were the works of Muḥammad ibn Mūsā al-Khwārizmī [3] (On the Calculation with Hindu Numerals, c. 825) and Al-Kindi(On the Use of the Hindu Numerals, c. 830). Hindu–Arabic numeral system – Wikipedia

It was via these works that the numbering system spread to Southeast Asia, Africa and Europe. The Europeans further spread the system in their economic and colonial dealings around the globe. Note, however, that it is the placeholding numeral system that was the core innovation. The actual numerals in use were not the same in all places—and indeed are still not the same everywhere. While the numerals 1, 2, 3, 4, etc. are now used as an international standard, the Arabic numerals are still in widespread use (۱، ۲، ۳، ۴، ۵، ۶، ۷، ۸، ۹، ۰) as are the Brahmi or Indian numerals (१, २, ३, ४, ५, ६, ७, ८, ९, ०) and even Chinese numerals.

Why is the number system universal, while the writing system is not?

1. Mathematics is a universal language. Spoken languages (and their written forms) by contrast are not.
2. Every human language has a set of core users, specific phonemes and a historical pathway whereby it was borrowed or invented and then developed to fit the specific needs of the language for which it is used. There is no one, simple writing system that could be used for all human languages being spoken or written in the world today.
3. Universal phonetic writing systems such as the IPA (International Phonetic Alphabet, International Phonetic Alphabet – Wikipedia and UPA (Universal Phonetic Alphabet Universal Phonetic Alphabet) fail the simplicity test. While useful to linguists, they are far too complex to be usable by people on a daily basis. In other words, they fail in exactly the realm in which the universal numbering system succeeds.
4. People are often very attached to the written form of their language as a form of cultural, regional or religious identity. Documents and inscriptions from the past mean a great deal to people as historical markers of identity.
   

   In short, people speak a vast multiplicity of languages, use a smaller set of writing systems, and for the universal language of music use just a few systems and for the universal language of math, only one.