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2. Models and meaning
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Numbers-key concept of symbols with meaning |
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Numbers are an everyday part of our lives. Go to any department store and select something that you wish to buy. A price tag will normally be attached. Go to the check out area and pay with money or a credit card. Look at your watch and see you are running late. Drive home and make sure you do not exceed the speed limit. |
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| Because you use numbers so easily and effortlessly, the hidden mechanics and model of thinking behind numbers is often obscured or not even considered. But what are numbers really? and how and why do they work? | ||||||||
| For instance, an architect or accountant doesn't think twice about adding, subtracting, and manipulating numbers to achieve results. The numbers are utility objects that never break down. If a wrong result occurs, it is not because of inherent defect in numbers. Life on the other hand isn't as perfect. Our bodies continue to decay from the day of our birth until our eventual death. Nature seems less perfect and reliable than numbers. | ||||||||
| 2.4.1 | Decimal and hexadecimal | |||||||
| In a majority of countries on planet Earth, the standard numerical system used for measure and calculation is the DECIMAL SYSTEM- a system that uses defined symbols with meaning using the number 10 as a base unit for measure. Hence 100 cents to a dollar, 1000 kilograms to a metric tonne, etc. In contrast, the civilization of the United Kingdom and the United States of America continue to use a parallel system for the measure of nature- the Imperial Measurement System- a system that is many thousands of years old, dating as far back as the Sumerians (6000 years ago). This system uses number measurements such as a foot, a yard, a mile etc. What then of other measure systems and of the nature of the number systems today? | ||||||||
| For at the heart of every numerical system are symbols with meaning: a model- a collection of ideas. A duplicate concept to the concept of words. That is why mathematics is seen by many as a language- it is indeed a language- a language of thought, rather than words- a language of spoken communication. As we will see later, a type of mathematics is the natural language of nature. In some instances, human understanding of this version of mathematics is strong- in the case of genetic science, the imperial measurement system and space. Yet in others, our model of numbers sadly lacks a deeper understanding of the power and importance of certain number concepts. We attempt to define the basis of numbers here so that in later chapters, our understandings can be expanded. | ||||||||
| 2.4.2 | The development of concepts attached to symbols | |||||||
| What is the number 1 if it loses its meaning? Just a squiggly line on a page. So it is, the study of ancient civilizations has been a painstaking process in understanding what lots of squiggly lines on monuments, pyramids and clay tablets meant. What makes a number a number, what gives it its power is the meaning attached, not the symbol used. | ||||||||
| Therefore it is the concept of one, the concept of a self enclosed singular thing that exists, a single unit that is the power behind the symbol 1- not the symbol itself. The symbol performs the task of transmitting or receiving that meaning in context. In describing a list of items in a room, in describing a person who comes first in a race. In religious and philosophical arguments. | ||||||||
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Arguably the six most powerful concepts attached to numbers are: |
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| We attribute the Greeks with the discovery of the concept of infinity. Yet there is ample evidence that the concept was well understood by cultures much older than the Greeks 2500 years ago. What is interesting is the delay in Western Cultures of the introduction of (4) the concept of zero (nothing). Neither the Greeks, nor the Romans showed the use of this concept in their mathematical writings. The ancient Eastern cultures on the other hand, had been using the concept in their numerical systems for thousands of years. | ||||||||
| It wasn't until the mid 12th Century (CE) when a modified version of the Arabic numerical system was adopted by European Kingdoms that the concept of 0 and the symbol we use today appeared. | ||||||||
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In terms of no (5), the concept of balance, the Nordic cultures and again the ancient East had been using this concept in their mathematical systems for a long period- the concept of duality, Yin- Yang in harmony. There appeared a brief period from the mid 12th Century until the late 14th Century BCE where the concept of harmony was incorporated into the numerical system as a second meaning to 0. however, for some reason the concept lost favour and now no longer exists as a discrete symbol with meaning in Western numerical systems. It is why, the Yin-Yang symbol from the east has been adopted. |
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| In terms of imaginary numbers, the Western cultures have excelled, with the creation of negative numbers and a host of special symbols for measurements, constants and so forth. | ||||||||
| The symbol used to describe the concept of Pi, sum, calculus are all examples of concepts attached to symbols. | ||||||||
| Again these concepts provide us with tools in which to understand more the language of our own world and the natural world in which we exist. | ||||||||
| 2.4.3 | The development of Symbols attached to concepts | |||||||
| The ancient Greeks were voluminous in their writing and rewriting to their own method, concepts and symbols attached to numbers. They were the great standardizers. Aristotle and his students followed in the footsteps of their most famous colleague- Alexander the Great and gained access to the sum total knowledge of mathematical writings of the ancient world. Their success in standardizing and codifying mathematical concepts and symbols were so impressive, texts by such ancient knowledge schools as EUCLID, PYTHAGORUS and ARCHEMIDES have been standard texts for the past 2000 years today. | ||||||||
| Even today, the essential framework of Geometry, Trigonometry and Algebra remain ancient Greek in origin. If you ever remember initially struggling through the definitions used, you have the ancient Greeks to thank. The symbols they used were the symbols available of the day. Today, we have designed much more powerful symbols such as stop signs, access, airport etc. however, tradition and convention dictates that the same symbols are attached to the concepts. | ||||||||
| 2.4.4 | The development of numerical systems | |||||||
| It is not just the power of the concepts and easy identification of symbols that makes numbers what they are- it is the rules associated with them that creates on overall numerical system- a model. | ||||||||
| There have been and are many different numerical systems on the planet Earth. Currently there is natures numerical system and then there are a variety of human systems of numeration from Decimal (base 10), Hexal (base 6), Hexadecimal (base 16) etc. | ||||||||
| While computers thrive in the binary world of one, or zero, the world of nature appears structured on a different base closer to the number six. | ||||||||
| The more advanced cultures on the planet Earth today, recognize this and use both systems. | ||||||||
| There is ample evidence to suggest that both systems of numeration can be found throughout nature from the neuron (binary and decimal) to hexadecimal (life, cells, rocks, planets, stars) | ||||||||
| 2.4.5 | The concept of numbers as pure ideas | |||||||
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Whatever you think of numbers (symbols with meaning), they exist as the purest ideas within our sum knowledge- unblemished by philosophical and religious wars. They are what they are- pure ideas, pure models. |
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| We will discuss numbers at length further into this web site. | ||||||||
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