## 1. Mathematical Innovations (Theory)

- The “Digito-Decimal” or “Digital” definition of Decimal Numbers opens up new
*arithmetical*possibilities. - The distinction between “Last” and “Leading” Digits is critical in terms of “numerical dimensions” and ”Orders of Magnitude”.
- The liberation of Number from the Number Line into “Symmetrical Number Planes” is the first step to matching symmetries of quantum mechanics for modelling 3D realities.

## 2. Digital Implications (Practice)

- The cell of a spreadsheet for Number offers functionality that is far superior to paper:
- as
*count*across rows or columns - as horizontal or vertical
*axis*label - as
*‘player’*(summand or factor) - as
*result*(sum or product) - as
*‘quantum’*of a*‘visualisation unit’* - or
*‘quantifier’*of ‘measuring units’ .

- as

## 3. Smart Visualisations (Technology)

- Spreadsheet cells or
*‘visualisation units’*- are
*positioned*as a result of arithmetical calculations - can be
*formatted*for*visual*differentiation - can reveal
*geo-metric*shapes and patterns.

- are
- “Diagonal Sums” visualise the ‘multi-additional’ aspect of a sum of many possible summands.
- “Orthogonal Products” visualise the ‘single-value’ result of a product as distinct ‘positional value’.
- The “Ortho-Diagonal Nature of Digital Sums” visualises
*ratios*of numbers hitherto not seen.

In summary, the appearance of Prime Numbers in many numerical contexts is a demonstration of:-

- the different characteristics of
*sums*and*products* - the effects of
*shapes*as*visual**contexts*for numbers - the use of spreadsheets as a ‘canvas with functionality’.