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’ .
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.
- “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 “OrthoDiagonal 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’.