2019-09-01|Sunatori's Discipline (Mandatory Parentheses)

Potential Discovery or Invention

• The following crazy confusion can be avoided by mandating the use of parentheses.

• PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
  • 6 - 1 * 0 + 2 / 2
    = 6 - ((1 * 0) + (2 / 2))
    = 6 - (0 + 1)
    = 6 - 1
    = 5

  • 8 / 2 * (2 + 2)
    = 8 / (2 * (2 + 2))
    = 8 / (2 * 4)
    = 8 / 8
    = 1

• BODMAS: Brackets, Orders (i.e., powers and roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
  • 6 - 1 * 0 + 2 / 2
    = (6 - (1 * 0)) + (2 / 2)
    = (6 - 0) + 1
    = 6 + 1
    = 7

  • 8 / 2 * (2 + 2)
    = (8 / 2) * (2 + 2)
    = 4 * 4
    = 16

• BEDMAS: Brackets, Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
  • 6 - 1 * 0 + 2 / 2
    = (6 - (1 * 0)) + (2 / 2)
    = (6 - 0) + 1
    = 6 + 1
    = 7

  • 8 / 2 * (2 + 2)
    = (8 / 2) * (2 + 2)
    = 4 * 4
    = 16

• I wonder how many scientific papers, technical reports and engineering reports have been published inadvertently using such tainted computational algorithm...
  • Ansys?
  • COMSOL?
  • Maplesoft Maple?
  • MathWorks MATLAB?
  • PTC Mathcad?
  • Wolfram Mathematica?
  • ...

  Rolls-Royce's Mathematical Modelling & Simulation
  Talented engineers are using Excel and getting serious errors of which they are simply not aware. And errors build up more rapidly than you might expect.

  PTC Mathcad
  Software packages are extremely complex with so many options and "buttons" that errors are easy to make and hard to debug.

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"Sunatori, Go Simon" <GS.Sunatori@HyperInfo.CA>

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• 2025-10-15T16:59:10.000Z