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The Fascination of Numbers

 

The role of numbers in everyday life »

A brief history of number »

The desire to be prescriptive »

Origins of the database »

How to use the database »

Tell us if we have left out interesting numbers »


The Penguin Dictionary of Curious and Interesting Numbers opens with the following paragraph:

"Numbers have exercised their fascination since the dawn of civilisation. Pythagoras discovered that musical harmony depended on the ratios of small whole numbers, and concluded that everything in the universe was Number. Archimedes promised the tyrant Gelon that he would calculate the number of grains of sand required to completely fill the universe, and did so." (Wells 1997).  To this day, exciting discoveries are still being made about numbers and the relationships between them.

 

Useful Numbers for Busy Managers contains the numbers that are used to convey and communicate management theory and concepts.


The role of numbers in everyday life

The creation of the concept of number and number systems is one of the hallmarks of civilization. Numbers dominate our lives, sometimes positively, sometimes harmfully, and often in ways unknown to us. We cannot escape them, like them or not, love them or not. Throughout history, number and numbers have had tremendous influence on our culture and on our language. Consider the numbers one to ten and the words associated with them:

  1. Monologue – one person talking
  2. Bicycle – two wheels
  3. Tripod – three legs
  4. Quadrangle – four sides
  5. Pentathlon – five events
  6. Sextant – one sixth of a circle
  7. Heptagon – seven sides
  8. Octopus – eight tentacles
  9. Nonagenarian - ninety
  10. Decimal – a tenth


The word quarantine is derived from the 40 days isolation required before entering a city in plague-ridden 15th Century Italy, and the months September, October, November, December (referring to months 9, 10, 11 and 12!) curiously derive from the Latin words for seven, eight, nine and ten. The names of the months were so named because the Roman year started in March!

If you are really fascinated by numbers and number reference we would strongly recommend The Book of Numbers by Bill Hartston (1997). It is comprehensive, compelling and witty. We have drawn on it extensively throughout this book, acknowledging it where appropriate.


A brief history of numbers


Perhaps the earliest recorded numerals were probably recorded on Sumerian clay tablets dating from the first half of the third millennium (3400BCE). A special symbol was in use for the number 10, and gradually symbols were introduced for numbers between 1 and 10. Subsequently numbers greater than 10 were added. The Egyptians had hieroglyphs for the numbers 10, 100, 1000, and 10,000.

The system was later taken over by the Babylonians, who used a number system based on 60 (from which today we get our minutes and seconds used for recording time and in expressing latitude and longitude, for navigation and cartography).

Around the 5th century BCE, the Greeks evolved their own system. They used all the letters of the Greek alphabet, plus three borrowed from the Phoenicians, as number symbols. The Romans evolved the system with which we are familiar. The Romans could express all numbers between 1 and 1,000,0000 using only 7 symbols (I, V=5,X=10,L=50,C=100, D=500,M=1000) but the system was not suitable for rapid written calculation.

The system we use today is formed by the juxtaposition of just 10 digits (1-9, plus zero) and is referred to as Arabic. It was derived from the Hindus about 200BCE. It reached the Middle East in the 7th or 8th Century CE.

There are many different kind of numbers: Whole numbers that are expressed by one two three etc. There are fractions, irrational numbers, complex numbers and even transcendental numbers but it is beyond the scope of this paper to explain them, but if you are interested you should consult the fascinating book by Conway and Guy (1986) and the Penguin Dictionary of Curious and Interesting Numbers (Wells 1997).


The irresistable desire to be prescriptive

From the beginnings of recorded time, civilizations have been seeking principles, rules and laws, which if observed, would result in increased effectiveness or superior performance (George 1968). The early Egyptians, the Babylonians, Moses, and Alexander the Great all created sets of definitive rules (amounting to a system). George (1968) argues that Alexander (336-323 BC) probably created the first system of management. Since then there have been hundreds if not tens of thousands of books about management and management theory.

Useful Numbers for Busy Managers is also useful for consultants, students, and learners and curious people in general. It does not aim to be, and should not be used as, a comprehensive guide to management thinking, for which you should consult the comprehensive surveys such as those by Stuart Crainer (1996, 1996a).

Origins of the database

The significance of numbers, and some numbers in particular, e.g. seven, is of abiding interest to large numbers of people possibly reflecting a need for order or sequencing in the human psyche. Today, there are dozens of web sites on the Internet with “magical number seven, plus or minus two” in their titles.

There are many situations where a passing reference to something like Ducker’s 5 Certainties, Porter’s 5 Factors, or the 5th Discipline, and other number references, such as the 3 Is or the 3 Cs, suggest that a handy reference with authoritative summaries would be useful to many people.

Another reason for this database comes from the answer to this question: What do ladders, rings, steps, levers, competencies, roles, types, dimensions, pillars, secrets, habits, practices, disciplines, qualities, plateau, factors, and so on, have in common?

Answer: They are all words used to convey conceptual or theoretical models of human, or organizational, effectiveness that are organized around numbers. Most of the words listed above are preceded by the definite article followed by a number, e.g. the five disciplines, the seven habits, the four roles. The smallness of the number and the word ‘the’ imply prescription. Five and only five, seven and only seven, otherwise there would be six in the list or eight.

Larger numbers (e.g. Deming’s 14 points) do not necessarily have the word “the” in front, but the larger number would reasonably be taken to mean that the author’s list is complete or relatively complete because he or she would otherwise have made the list a bit longer. Again the inference we can draw is clear: This, and only this, is what the author thinks we need to know or, less generously, that is all they could think to say. Very large numbers, such as 101 ways to do things, also imply completeness on the part of the author.


How to use the database

Useful Numbers for Busy Managers is a handy reference. All you now need to know is a number or a name, e.g. the 4 Rs or the 6 thinking hats, to find your way to an authoritative summary with a full reference to the original source. The summaries are not intended as a substitute for reading the full book or article, but they will help you decide, and may well stimulate you to seek out the full text.

In this database, you will find numbered:

Pillars, Ladders, and Steps
Stages, Theatres, and Phases
Mistakes, Myths and Failures
Attributes, Characteristics, and Traits
Dimensions, Factors, and Elements
Competences, Skills, and Disciplines
Habits, Hallmarks, and Plateaus
Rules, Principles, and Laws
Certainties, Dilemmas, Pre-conditions and Mega-trends
Roles, Tools, and Processes
Strategies, Priorities, and Forces
Rings, Keys and Building Blocks
Schools, Types and Styles


In addition, you will find the letters A, C, F, I, L, M, P, R, S, T are all featured because they are all numbered in an explicitly or implicitly prescriptive way. (Curiously, we have found no entries for other letters.)

The database can be browsed. Wander through it and see what turns up. Explore at random and discover the ten most powerful two-letter words, or the seven Ss of self-managed learning, or the thirteen thinking tools of the world’s most creative people.

Useful Numbers for Busy Managers can be searched by theme. If you are interested in Team working or in Leadership, you can go straight to the three, four, or whatever dimensions, traits, characteristics, etc. of leadership or team working. The ease of making direct comparisons is particularly interesting when competing authors’ use of number implies or actually states prescription, i.e. these are the dimensions, skills, competencies, roles, etc of leadership, or the six characteristics of, for example, a learning organisation.

The  thematic sections, allowing direct comparison of prescriptive models and concepts that are organized around number, are:

  1. Business and organizational effectiveness - the nature of successful organizations
  2. Business and organizational effectiveness - how to achieve competitiveness and profitability
  3. Business and organizational effectiveness - mergers, alliances and partnerships
  4. Careers and career development
  5. Change and change management
  6. Communication
  7. Culture - national
  8. Culture - organisational
  9. Human nature
  10. Innovation and creativity
  11. Leadership
  12. Learning
  13. Learning organizations
  14. Management theory
  15. Management development
  16. Motivation
  17. Personal effectiveness
  18. Teams and team-working

Tell us if we have left out interesting numbers

We are sure to have omitted famous numbers, but not intentionally. If we have do let us know and we will incorporate them and acknowledge your help.

 
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