Nat Notation

This is a page exploring Nat Notation, a way of writing the natural numbers invented by Nat Alison.

Their original conception is more calligraphic, which is extremely cool, but here I explore a similar form that is easier to generate using web technology.

The system is simple:

• The number 2 is a circle.
• Primes are a circle around either the preceding or following number, so 3 is a circle around a 2; etc. Solid circles mean you're incrementing the contained number; dotted circles decrement. (Which you use is an aesthetic choice; I try to minimize the size of the number.)
• Composites are first prime-factorized; each prime in the factorization is written with the prime above the exponent, and all the factors together are written beside each other. In other words, vertical juxtaposition is exponentiation, while horizontal juxtaposition is multiplication.

  So, 4 is a 2 above a 2; 8 is a 2 above a 3. 6 is a 2 next to a 3. Etc.

• The number -1 is a dashed circle. Fractions are numbers raised to the power -1; roots are numbers raised to a fraction power.
• Addition is horizontal juxtaposition with a dash separating/connecting the terms. (To subtract, negate the second term.)
• Rarely, parentheses are required, for readability if nothing else. They are represented by an open-topped rectangle.