The tendency of gradually improving systems to undergo a sudden large increase in functionality, becoming universal in some domain.
The first Universal System we know of was DNA. All organisms on earth are encoded with the same alphabet of DNA bases, just using different combinations.
Universal systems have been invented a few times throughout history but always by accident. Nobody realized their significance until decades, sometimes centuries later. Only since the Enlightenment has the significance of universal systems been recognised and sought after.
Take Egyptian hieroglyphics for instance. Every word is represented by its own hieroglyph. To invent new words you need to invent new hieroglyphs (and then teach everyone what they mean). It's a non-universal system.
As the rules for writing systems were improved we moved from specific word-level abstractions to letter-level abstractions. Latin-based alphabets were capable of representing every word in the language. Thus, a jump to universality.
Roman numerals were an improvement upon tally systems for performing basic arithmetic, but they weren't universal. The number one thousand was represented by the symbol ↀ, and that was their highest number. To calculate anything higher than that means appending ↀ's to each other, and then you're back to tallying. The only way to progress arithmetic beyond tallying is with rules of universal reach.
As with alphabets, a small set of rules is enough.
The numeric system we used today has ten symbols, the digits 0 to 9, and its universality is due to a rule that the value of a digit depends on its position in the number. For instance, the digit 2 means two when written by itself, but means two hundred in the numeral 204. Such ‘positional’ systems require ‘placeholders’, such as the digit 0 in 204, whose only function is to place the 2 into the position where it means two hundred.
The power in universal systems comes from their Reach. They can do a lot more than they were intended to do. A clear example of this is the computer in your washing machine. Given enough memory and time there is nothing preventing it doing astrophysics calculations.
Our brains are universal systems. We are capable of explaining anything.
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