Posts Tagged ‘classification’

Why Numbers are Waves

Wednesday, September 3rd, 2008

Pythagoras, the inventor of the Music of the Spheres, thought that the principles governing Number are the principles of all things.There are many principles behind the Numbers. The most intriguing is called the Riemann Hypothesis. It defines a spiraling relationship between the Prime numbers.

What is a Number?

A Number is a Symbol that represents an Object we use to Count and to Measure. The Number-Object 1 is often represented by the symbol “1″ and the sound “One”.

When we Count we are able to Tell How Many Objects are available in a certain Set. In mathematical terms the Amount of Objects in a Set is called the Cardinality.

To define a Set we have to define “What the Objects Are”. If we don’t do this we are not able to See, to Observe, the Objects. To Count we have Define “What we are Counting“.

To define what we are counting we have to Classify and to Describe. To Classify we have to Name. The name “Sheep” is connected to a Mental Picture of something that “looks like a” Sheep.

There are Names who are not represented by a Mental Picture. An example is the name “number”. This Class of Objects contains Abstractions of Real, Visible, Objects or of Actions that are Performed on Visible Objects. Abstract Objects/Actions are related to, Mapped, to Visible Objects/Actions by Metaphors. One Apple “is representing” the Number One.

There is no fundamental law that Tells us How to Classify. Classifications are highly Culture and Time Dependent. The effect is that different people will count different amounts of objects when they don’t agree about “What they are Counting“.

When we have Counted a Set of Sheep we are able to Add when we have counted another Set of Sheep at another Place. We are only able to Add when the Sheep at both places are “the Same“.

It is impossible to add Sheeps and Cows unless we define a more abstract Set called Animals. Again the problem of classification arises.

When we want to Count Every Thing we have to find the Cardinality of The Set of All Sets. The Cardinality of this Set is “not knowable“. Most scientists would say that the cardinality of this set is infinite (“not bounded“). Mathematicians would say that this Set maps to the Set of Numbers or to a Sub-set of the Set of Numbers. The paradox of Russell shows that the Set of all Sets “does not exist“.

It does not matter in what order we Add Numbers. A+B = B+A. This is called the Commutative Quality of the Numbers. Remember that this Quality only applies when we are counting the Same Objects

Another Quality of Addition is called Associativity. It does not matter in what order we add a sequence of numbers. 1+(2+5)+3 = (1+2) + (5+3). Remember that this Quality only applies when we are counting the Same Objects.

 When we are Counting Sets of Sheep that contain the Same Amount of Sheep we are able to create a new operator “*” called Multiplication. Multiplication is a Repetition of the Same Amounts (another word for Cardinality) of Counting.

When we Multiply the same Qualities of Addition are applicable. Multiplication is Commutative and Associative. 6*7=7*6 and 6*(7*8)=(6*7)*8.

 What is a Prime?

We have finally reached the Primes. A Prime is a Number that can only be divided by 1 and Itself OR Every Number can be written as a Multiplication of One or more Primes.

Mathematicians Think that the Set of Prime Numbers is the Foundation of the Set of Numbers.

Nobody thought that this Foundation contains another Foundation until Riemann formulated his famous hypothesis. Riemann observed that the frequency of prime numbers is very closely related to the behavior of the so called Riemann Zeta function, ζ(s) = 1 + ½**s + 1/3**s + ¼**s + . The hypothesis is still not proven but is verified by computer programs that generate very big numbers (1,500,000,000) and until now it still holds.

The operator “**” is called Power or Exponent. It represents a Repetition (s) of the multiplication of the same number. 2**2 = 2*2=4. The operator “/” represents the operator Division. Division is the “opposite” of Multiplication.

A Foundation is something that is used to build on. It is the “lowest” layer of all the layers. If a Foundation contains a Foundation many theories that were formulated using the old foundation are at stake. One of the most important theories is the theory about the Numbers themselves. If the Numbers are not what they are thought of new mappings, new metaphors, are possible. In this blog I will try to explain that Numbers are not Distinct Isolated Objects. Numbers are not Parts.

Numbers are Waves.

The Primes are the Foundation of the Number System if we Accept that:

  • A Number is something we use to Count Objects
  • We are Counting the Same Object
  • Multiplication is Repetitive Counting
  • the Quality of Commutativity in Multiplication and Addition Applies

We are not Counting the Same Object at All.

We are always Counting Cows and Sheeps because every Object is Unique. If we make a Picture of one Sheep we see a Lot of Detail. We ignore these details because we are not interested in them when we are Counting Sheep. The Sheep are treated as Objects.

When we want to Articulate the Details of One Sheep we Run Out of Words to describe all the details. We are unable to define all the attributes to classify all the details.

When we are Counting, Every Thing has to be treated as an Object because Counting implies the Perspective of the Object.

The Quality of Commutativity in Multiplication and Addition does not Apply.

If we want to treat Every Thing As It Is, the Commutative Law is not applicable: A+B is not equal to B+A. When we want to treat Every Thing As It Is, Every Thing is One. If we Map every Unique Object on the Number Line every Number is representing a Unique Object. A Number is a Unique Key, An Identifier.

If we are not able to Add we are not able to Multiply. If we are not able to Multiply the Primes are non-existent. If we accept that Every Thing is Unique we are not able to Talk about Anything. We have be Silent and Observe. We could also accept that Language is a Funny Game We Play (Wittgenstein) or Accept that a Picture Paints a Thousand Words.

When we want to Quantify or Qualify we are always Equalizing.

When we want to Count we have to accept that we have to make Some Things the Same when they are really not the Same. If we want to Quantify we have to accept that we are making Mistakes all the Time.

If we want to Qualify we have to accept that Numbers are not usable. If we want to Qualify we have to accept that Classifications are not usable. If we want to Qualify we have to Accept that somewhere we are using the Numbers and are Quantifying.

When we use Language to Qualify somewhere we introduce concepts like High and Low and are forcing an Order on Reality. The only thing that is left is to use the Emotions to do this. We could Say that Every Thing is Beautifull and produce a Sound (“Ahhhhhhhhhhh” or “Wauw“).

When we want to Quantify or Qualify we have make sure we are not equalizing something that is really unique. We have to Make a Choice and think about the Consequences. If we define a Selection Criterium or Define an Attribute of a Unique Object or Define a Filter, we have to be aware that the Attribute simply defines a new Object. This Object is always an Abstraction. When we define the Attribute or Quality of Race we Divide Reality in Races.

Language always Divides The Whole in Parts.

Multiplication is Repetitive Counting.

When we Multiply we make use of two Types of Numbers. We are using a “repetition factor” and we use a “counting factor“. These types of Numbers are not the same. When they are not the same the Commutative Law is not applicable. 7*6 is different from 6*7. The first statement is about 7 times a Set of Sheep with Cardinality 6. The other is about 6 times a Set of Sheep with a Cardinality of 7.

Primes are Frequencies.

A Repetition Factor could be defined as a Frequency. If we move from the domain of the Rectangular frame, Cubes, to the Circular frame of Mathematics, Waves, the Riemann Hypothesis changes into a statement about the Musical or Harmonic Behavior of the Primes. The primes have Music in them. You can even Listen to this Music. Pythagoras was Right.

If Primes are Frequencies What are Numbers?

If every Number is a combination of one or more Prime Numbers, every Number contains one or more repetition factors. If we move to the Circular Domain, Multiplication changes into Addition. A Number is the Sum of Waves. A Mapping from the Rectangular to the Circular Domain is called a Fourier Transformation.

If Numbers are Waves what are Objects?

Objects are also Waves.

If Objects are Waves is there a Boundary between Objects?

No. They are All One. In a Circular World there is no Beginning and there is no End. In a Spiraling Spiral World Everything is Closed in Itself. We are an Enfolding of the One that is Closed in Itself. The One is Aware. It is Consciouss. Every Thing Contains a Conscioussness, A Spark of the One.

What is Behind Every Thing?

0. It all starts with the Primal Void, 0.

1. Out of the Primal Void the One is Created. The One is The Mover that Moves Itself, The Center. It Enfolds in Itself.

2. The One is Observing Itself so there are Two. The One becomes Conscious.

3. The Two Expand and Compress so there are Three, the Trinity. The Two are named Control and Desire. The One, Conscioussness, stays in the Center. The One Voids the Two (-1 + 1 = 0).

4. The Two are split in Two so there are Four Forces or World Views. Control and Desire are “compensated” by Spirit and Soul.

5. The One, Consciousness, is always in the Middle. Now there are Five, the Pentagle. The Five are called the Hu-Man. It contains Control, Desire, Spirit (Creativity), Soul (Love, Emotion) and Conscioussness. The last part connects the Human to the One. A Human is a Dynamic Instability where the Four Forces are constantly trying to find Harmony. The Conscioussness Observes and Reflects. It helps the Forces to find Balance.

6. The Four Forces combine. There are Six or Twelve combinations. This depends on the way the combinations are made. Four independent Forces generate 1*2*3 combinations when the Combinations, the Relationships or the Mappings, are considered Unique. When a Relationship is a Two-Way Connection (A Dialoque), the amount of combinations is 2* (1*2*3) =12. Six is the first Perfect Number. The Sum and the Product of its Divisors is Equal. 1+2+3 = 1*2*3.

7. The One is always in the Middle so there are 6 + 1 = 7 Relationships. There are Seven Chakra’s. The Chakra in the Middle, The Heart, is related to the Centre, The One (-3,-2,-1, 0, 1, 2, 3).

9. This is a Pattern where the Four Forces are connected in a Circular Pattern. One Pattern moves with the clock and the other counter the clock. The complete pattern looks like a Moebius Ring

10. This is the Lowest Level in the Sephirot, The Tree of Life. It is called Malchut, the Kingdom of God. It exists outside the Pattern of the Nine.

12. See 6. The four Forces are now in their Dialogic State. 12 is a Highly Composite Number (HCN). A HCN is a Social Number. It contains Many Divisors. HCN’s are used in situations where many divisions are needed like Clocks and Calenders. HCN are used to avoid conflicts. Other HCN’s are 24 (hours), 60 (seconds) and 360 (degrees).

There are twelve signs of the Zodiac, twelve Tribes of Israel, twelve Apostles of Jesus and twelve Houses in Astrology. Every number is a Relationship between Two Powers of the Four Powers and can be interpreted as such. The Four Powers are the cornerstones. Examples are the Apostles John (Spirit, Eagle), Marc (Control, Laws. Lion), Luc (Desire, Bull, Ox) and Matthew (Soul, Human/Angel).

13-24. With the Thirteen a new Cycle on Another Level Starts. The 13th Card of the Major Arcana of the Tarot is called Death, a New Beginning. The Soul has travelled in the UpperWorld (Earth, 1-12, Our Material Reality) and moves to the Under World (Heaven, The World of Souls, 13-24) to Clean itself and to start a new Cycle as the Fool (0).

The Tarot spelled as TARO-T is a Cyclic Structure that operates on Three Levels. In every level the four Forces (T, A, R and O) are combined in different ways. The Highest Level is called the Major Arcana and contains 24 (1*2*3*4) Cards. The last card indicates the End of the Cycle of the TARO. Every card in the Higher Arcana is named with a Permuation (without Repetition) of the letters T,A,R and O.

25-36. The Second Level contains 12 Cards (3*4). The King, Queen, Knight and Page represent the four Forces.

37-76. The Third Level (40 Cards) contains the Ace (1) and the numbers 2-10. The four Forces are called Sword (Mind, Control), Cups (Soul, Emotions), Wands (Spirit, Creativity) and Pentacles (Senses, Desire).

 The One Enfolds into a Spiraling Spiral.

New Numbers and New Levels are Created.

We are One AND we are Many. We are The Same AND we are not The Same. We are Music AND we are Producing Music. We are Repetitons AND we are Creating Repetitons. We are Primes AND we are not Primes.

LINKS

Chaitin, About the Russell Paradox and other Controversies concerning the Foundations of Mathematics

Listen to The Music of the Primes

About Noncommutative Geometry

About the Same and not the Same

A Book about The Music of the Primes

Explaning the Riemann Hypothesis

Every Thing You want to know about The Riemann Hypothesis

How the Baby Boomers stopped their own Revolution

Tuesday, September 18th, 2007
The Baby Boomers when they were Young

The Baby Boomers when they were Young

When I started to work in 1976 I never heard of something called HRM. My boss hired me.

He discussed my salary and gave me the assignments.

The salary of my colleagues was a secret. I also did not know why my salary was raised. It just happened.

Three years later I was promoted to manager (group leader). I was very surprised this happened.

My new manager (called a section leader) handed me the files of my employees. I had to take care of them.

They contained many secret documents about what the former managers thought about the employee. At that time the managers talked about the employees in complete secrecy.

We, the New Managers, did not like that. We opened up the secret files, destroyed the ”not-objective” data, standardized the data and put the data in a Database later called a HRM-System.

Suddenly I was the one who was responsible for hiring and firing. Every group-leader was different. I was always very open to my employees. We worked as a team to create and maintain software-systems.

I loved to program and design and I never felt the need to stop this. Managing my group was simple. It took about 1 day a week. In this day I had to attend meetings with other managers.

Other group-leaders (mostly much older) were spending all of their time managing their group. I soon found out that they were really managed by their group. They were unable to resist the informal power of some of their employees. When the new salaries were fixed some of them got a lot of money. This became known in my group and I got into trouble.

Why is he paid more than I am paid? He is really doing nothing!

I went to talk with my colleague but he did not want to talk. I talked with my section-leader and I found out that my colleague was his personal friend. He “covered his ass“.

At that time there was a big difference between an employee and a manager. When you became a Manager you became part of an Elite with its own Privileges and Culture. The most important Rule was that people of this Elite always covered the ass of the other members. We, the New Managers, did not like that and we started to destroy the Old Management Culture.

The other group-leaders experienced the same situation. We started to talk about this issue at our Section-meeting. After many discussions we went to talk one level higher (the director). The end result of all our actions was a revolution. We removed all the old powers and took over.

This also happened when I was a student. I was part of the baby-boom-generation that reorganized society. We were the revolutionaries that wanted to create a better society based on the principles of the new age of Aquarius.

Now almost 30 years later my old colleagues and I have created a System that is blocking everything they stood for. Just like my section-leader they want to stay in power.

The Baby Boomers when they were Young

The Baby Boomers when they were Young

The big difference between 30 years ago and now is that the New Revolutionaries have to change a (Software) System. It is impossible to detect the Human Cause of all Evil.

We,  the Baby-Boom Managers have standardized almost everything. The Systems have taken over Control and the Sad Thing is that almost nobody knows what the Systems are really doing. They live a Life of their Own.

It is almost impossible to reach consencus because many many specialized managers are involved and they all defend their own territory. The Sad Thing is that almost nobody knows what their Territory really is about.

Everything is Magically connected to Everything Else by the PatchWork of Overlapping Systems. A Problem in One Area suddenly comes back in a completely different Area.

The only way to accomplish something is to play the Game of Politics. To play the Game of Politics you need to make friends and you have to stay in the right coalition.

To do this you sometimes have to abandon your friends to reach the Goal. The effect is that nobody trusts nobody anymore or friends are covering the Ass of their friends. The effect is that many incidents are covered up. The effect of the cover up is that many people don’t know what is really happening or (worse) many people know what is happening but discuss the issues in a secret place.

The effect of this is that many people are not working at all. They are gossiping all the time. The effect is a loss of productivity and the only Solution we can think of is to implement more Systems.

The most important effect is a Change of Focus. The focus is directed inside the Company and not outside the Company. Outside the Company somebody is providing the money to play the Game. He or She is called the Customer.

The Systems have transformed the Customer into a Standardized Object stored into a Computer.

The Systems have completely Blocked the View on the most important Asset of a Company, the Human.

What Happened?

We developed a system that wanted to treat Everybody the Same Way.

How did we do that?

Step 1: Classify what everybody is doing (programming, designing, project-management …).

Question: When somebody is capable of everything (a talent) what do you do?

Answer: Always start with the lowest classification in this way people believe work is moving Up.

Step 2: Define a Career Path.

Step 2.1. Define Low (junior), Normal and High (senior). Take care that this is a normal distribution. If you do that people keep the believe that a Senior is better than a Junior!

Step 2.2. Define importance. A designer is more important than a programmer. Manager is more important than designer.

Question: Why is a something more important than something else?

Answer: Something is more important when we pay a higher salary. If we do that people start to believe that money is the most important motivator.

Effect: Everybody wants to become a manager because a manager is the best! The negative effect is that a manager does not like the employees in his department who are better. They are his competitors.

Step 3: Define a test to prove you are allowed to move to the next level.

Question: What defines a talented programmer?

Answer: He has finished his training.

Effect: Employees have to spend a lot of time to pass exams. Training becomes more important than experience. People start to act out of the book.

Step 4: Create specialized departments (Training, Security, Data Management, ..).

To save money we started to train people outside the company. The teachers did not have any experience. They knew what was written in the books that were written by people that did not have any experience in the field they were teaching.

Later the teachers changed into consultants and started to tell the employees and the managers how to do it. Doing the trick is easy. Inventing new tricks and implementing the new tricks becomes very difficult. You have to convince many managers.

Effect: Innovation is tricky bussiness. You have to take a risk and when you fail you are out of the carreer-race. Old approaches are implemented with a different name.

Step 5: Create departments that are testing if the employees are doing what the trainers told them to do (Quality Management). When they don’t do what the trainers told them to do we just don’t promote them.

Effect:

Everybody is Equal.

I hope you see what I am trying to show you. By treating everybody the Same Way we finally have created the Same People. The top (talent) and the bottom (sick, problems at home …) are gone.

We have Equalized the Population.

The steps 1 to 5 are not the only steps. The System has improved itself all the time.

Before the division employees took care of other employees. We have designed a special approach to take care of the sick and other causalities. This has given them a negative status. The effect is that some of them deteriorate and others are afraid to tell what the matter is. They go one when they are sick or they ignore the problems at home. The effect is more problems at home and/or stress-related diseases (Burn-Out).

We have divided managers in groups. Some of them manage resources (!) other use the resources. The effect is the loss of the team-mentality.

We have divided resources into internal and external resources. We hire them from a specialized company. The effect is a loss of company-pride a higher level of the team-mentality.

We have automated almost everything to speed up efficiency. The effect is that we have to know the number (the unique identifier) to know about people. We are unable to enter unique information about a person. They are standardized on a higher level.

We have created a special department called HRM. They are managed top-down. The effect is that at every level we are unable to create a unique solution for a unique situation.

The Baby Boomers when they were Young

The Baby Boomers when they were Young

What To Do?

Work in teams.

Start to talk with the employees again. Be honest and open.

When you feel somebody is special give him a special treatment. Explain this to everybody.

Don’t be afraid to take responsibility for what you have done. Admit mistakes.

Don’t store everything in a database. Forgetting something is a positive thing. It makes is possible to start all over again.

Don’t specialize too much. Get rid of all the departments that are too far away from your primary process, servicing the customer.

Rotate. Don’t keep a person too long in a specialized job. Give experienced people a change to teach or to specialize but never keep them in this job for long.

Stop politics. Never allow that people are playing games with people. Fire people who are playing dirty games.

Surprise people. Don’t plan careers. Give everybody the idea that everything is possible.

Stop the gossiping. Give everybody a change to tell what they don’t like and listen.

Demote. When somebody is incapable to do his job give him the job he is capable of and give him the salary of the job. This stops the expectation that everything always has to move up. When somebody gets into trouble when he is demoted make an exception.

Give employees a chance and the time to help other employees.

Don’t hire too much people outside your company. Give priority to teach your own employees to learn the trick of the outside specialists.

Give your own people the time and the tools to innovate.

Hire outside specialists to do the things that are already stable and repeatable or better automate these activities. They are most of the time very boring. This is a very usefull indication to use IT.

LINKS

About Long Term Cycles

About Vocation

About the Calvinistic Work Ethic

How to Destroy your Company by Implementing Packages

How the Baby Boomers were Educated

About Knowledge Workers

About the Effects of the French Revolution

Why the Industrial Revolution was a Social Revolution

About the Struggle of the Classes