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.
Chaitin, About the Russell Paradox and other Controversies concerning the Foundations of Mathematics
Listen to The Music of the Primes
About the Same and not the Same
A Book about The Music of the Primes
Explaning the Riemann Hypothesis