A Basic Engineering Tool: Numbers

Physically, a number is establishes a relationship to the physical world.  By itself, a number is pointless. Think about it, a number is nothing more than a symbol, or a representation of something else.  A number is only relative to what it is defined to be.  In our world, a system of numbers is used to define a specific physical system.  For instance, the size of an object can be described by anything we want to relate it to.  I could describe the size of my desk as an arm deep by a leg tall by a leg wide.  Mathematics allows us define an effective system of universal numbers (representors of the physical world) and methods to relate each number to each other.

-Addition can be view as a method to build a system of more than one number

-Multiplication can be viewed as method of building a system defined by at least two instantaneously constant numbers, or constructing a set of equivalent numbers a constant number of times

-Integration can be thought of as an multiplication on steroids; a way to build a system of numbers that allows us to combine changing numbers at a changing number of times.

The point: addition, multiplication, and integration allow us to build sets of numbers.

-Subtraction can be viewed as a way to deconstruct a system of numbers (although this does not explain negative numbers, negative numbers are essentially only relative to the system they are placed into aka defining position, velocity, money.  Negative numbers cannot describe a physical quantity since mass cannot be created or destroyed.  essentially, negative numbers can only be used to define direction)

-Division can be viewed as a way to disassemble a system of numbers into at least two instantaneously constant numbers, or deconstructing a system of numbers into a set of equivalent numbers previously constructed by a constant number of times.

-Differentiation is division on steroids; a way to disassemble a system into two of its constructing number components

The second point: subtraction, multiplication, and integration allows us to take apart sets of numbers.

A quote by Albert Einstein: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." (from Wikipedia)