Posts Tagged ‘Venus’

About the Vedic Square

Monday, December 19th, 2011

This blog is about the Cycle of Nine implemented in the Digital Root or Modulus 9-Function. The Digital Root generates many Patterns that were used in Ancient Architectures.

One of the most important Digital Root Patterns is the Vedic Square. It is the Digital Root of the Multiplication Table of the numbers 1 to 9.

This Table contains the Harmonics of the Numbers 1 to 9. These Harmonics are highly related to the Harmonic Pattern behind the Cycles in our Universe.

The first part of this Blog is about the Digital Root. It contains the patterns that are behind the Cycle of Nine.

This part is very technical but it makes it possible to show that there is a deep structure  behind the Modulus-9.

This pattern has to do with just two numbers, 2 and 3. They generate the Spirals of Expansion and Compression of our Universe.

2 and 3 and their Sum 5  are also the Numbers behind the Harmonics of our Universe.

The Second Part is about the Vedic Square. It is called the Vedic Square because this Square is one of the most important tools in Ancient Vedic Mathematics.

Vedic Mathematics was used in many Ancient Cultures (China, Egypt, Greece) with different names. The Chinese art of Feng Shui was called Vaastu Shastra in India.

Pythagoras, trained in Egypt (Heliopolis),  used the same principles and used the same  Patterns the Ancient Vedic Scientists were using.

The last part is about the Game of Chess. This game is  just like many other Ancient Games a Simulator of the Game of the Universe.

This blog contains many links to other Blogs and Resources on the Internet. These references make it possible to dig deeper into this fascinating subject.

About the Digital Root

When  you divide a number X by a number N the Remainder of the division is called X Modulus N.  22 mod 7 = 1 because 22 = 3×7 + 1.

The Modulus-function N maps the Set of the Natural Numbers to the Numbers 0, 1, 2, ….,N-1.

One of the most famous and ancient Modulus-functions is called the Digital Root. The Digital Root is the Modulus 9 function.

Because 10 mod 9 = 1 every Power of 10 has a Modulus 9 of 1. Therefore (a10**X+ b10**Y+…) mod 9 = a + b, the Sum of the Digits of the Number. 62 mod 9 = 6+2 = 8.

Digital Roots have been recorded for thousands of years, formalized by Pythagoras in 530BC and even earlier in Indian Vedic Mathematics (Vaastu Shastra).

Digital Roots are used in Numerology. In Numerology Numbers have a Meaning.

In Gematria Letters and Words are transformed into Numbers which have a meaning.

In Ancient Languages like Hebrew Letters are also Numbers. Numerologists believe that Words with the same Digital Root have the same Meaning.

The numbers 0 to 9 of the Digital Root are the Points of the Tetraktys of Pythagoras.

The Tetraktys of Pythagoras

The Modulus 9 pattern contains 2 number groups (3,6, 9) and (1,2,4, 5,7,8).

Later we will see that the last group contains 2 subgroups (1,4,7) and (2,5,8).  Together with (3,6,9) we can map these 3 Triangels on the Modulus 9 Circle.

4 is the Middle of 1+7=8, 5 is the Middle of  2+8=10 =1 and 6 is the Middle of 3+9=12=3. 5 is also the Middle of the Middle.

The group (1,2,4,5,7,8 ) is called the Ring Z/9 in Mathematics. Z/9 is isomorphic with the Sequence 2**N mod 9 where N is positive and negative. The sequence 1,2,4,8,16(7),32(5),64(1),128 (2),256 (4),… repeats itself until infinity.

This Sequence is the Expansion and Compression Pattern of the Number 2.

The Ring Z/9 is part of the Tetraktys and forms a Hexagram. This Hexagram is a 2D-projection of the Cube of Space. When we combine the (3,6,9)-pattern with the Hexagon a (4×4) Triangle is created.

The number 2 is the Container, the Cube, inside the Tetraktys. That is the Reason why the Second letter in the Hebrew Alphabet Beth means Vessel or Container.

(3,6,9) is a Triangular Cycle that repeats itself until Infinity.  The Number 3, the Trinity, is the Mover of the Container of 2. This Rotation moves With and Against the Clock.

This is the reason why the 3th Letter of the Hebrew Alphabet, Gimel, means Camel. The Camel of Gimel carries the Water into the  2 Containers of Beth.

The Number-2-pattern contains 3 Binary Groups (called Polar Pairs) with a Sum of Nine (1,8), (2,7), (4,5). The Number-3-Pattern contains 2 Polar Pairs (3,6) and (0,9). The Polar Pairs represent the Lines of the Tetraktys.

(0,9) maps unto Itself and represents The Beginning and The End, The Now. (0,9) is a Point and a Line.

The Polar Pairs of the Z/9 create a Cyclic Pattern that contains two Squares, (1,2,4,0) and (5,7,8,0). Both of them Share the Zero, The Void.

The Sum of the Opposite Numbers of the Z/9, (4,8 = 12=3), (1,5 =6 ), (2,7=9) of the Tetraktys shows the 3,6,9-pattern again.

There are 8 Ternary Groups ((1,5,9), (1,6,8), (2,6,7), (2,5,8),(2,4,9),(3,4,8),(3,5,7),(4,5,6)) with a Sum of 15. This Ternary Group represents Triangels. All of them are part of the famous Lo Shu 3×3 Magic Square.

The 3 Triangles of (1,4,7), (2,5,8) and (3,6,9) copied from the linked Website.

When we use the number 3 as a generator 3 Triangles are created (1,4,7), (2,5,8) and (3,6,9).

The 3 Triangles move With and Against the Clock ((1,4,7) and (7,4,1)).

It takes 3 rotations to get every Triangle back to its original position. (1,4,7) becomes (7,1,4) and (4,7,1). This means that there are 6 permutations of every Triangle.

Every addition of two Triangels produces another Triangle.   An Example:  (1,4,7) + (2,5,8) = (3,9,6).

When we create a Matrix to find all the combinations a new group of 9 transformations ((1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,6,6),(7,7,7),(8,8,8),(9,9,9)) appears. They are the Triangels that are a Line and a Point. An Example:  (1,4,7) + (1,1,1)=(2,5,8).

There are now (18 +9=27) x27 = 729=3**6 = 9**3 possibilities.

The same 27×27 Matrix appears when we Multiply the 3 Triangels. An Example:  (5,8,2)x(5,8,2)= (25,64,4)= (7,1,4) and (3,6,9)x(5,8,2)=(15,48,18)= (6,3,9).

Another interesting patterns  becomes visible when we look at the Opposite Numbers of 3 Triangels (1,5), (2,6), (3,7),(4,9) en (5,9) in the Picture above.  They recreate the Triangels. An Example: (5+9=5, 2+6=8 ,8+3=11=2).

About the Digital Root of the Golden Mean

The 27×27 Matrix pattern also emerges out of 24 repeating numbers (1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9) of the Digital Root of the Fibonacci Sequence (The Golden Ratio).

this solution gives the densest
lattice packing of spheres in 24 dimensio

When we group the Golden Ratio pattern in 2′s (2×12) the Polar Pairs appear. The 12 pattern has  a Sum of 108 = 0 Modulus 9. 108 and 24 are related to the Gayatri Mantra.

1 1 2 3 5 8 4 3 7 1 8 9

8 8 7 6 4 1 5 6 2 8 1 9

When we  group the pattern of 24 numbers (3×8) of the Golden Ration into Trinities the Triangle Pattern appears again.

1   2  3  4                  -3 -2 -1 -4 (Pattern-number)

1   1  2  3  (7)           5   8   4   3   (2)

7   1  8  9  (7)          8   8   7   6   (2)

4   1  5  6  (7)          2   8   1    9   (2)

The Pattern of the Pattern is (1,2,3,4,-3,-2,-1,-4). The last part of the Pattern (-3,-2,-1,-4) can be transformed into the first part (1,2,3,4) by adding 4.

The Digital Sum of the first 3×4 numbers is 7 and the Digital Sum of the last 3×4 numbers is 2.

When we rearange the 24 cycle in 6 groups of 4 digits another pattern shows itself: (1,4,8,5), (1,3,8,6), (2,7,2,7),(3,1,6,8), (5,8,4,1), (8,9,1,9).

The pattern of the Golden Mean copied from the Linked Website

When we combine all the different rotations of the 3 Triangels a Cyclic Flow Pattern appears that looks like the Jitterbug of  Buckminster Fuller.

The Jitterbug is a 3D projection of the 4D 24-Cell (again 24!) also called the Hyperdiamond.

The 24-cell is self-dual and is the regular polytope with no analogue among the five Platonic solids of 3-space.

The 24-cell also called the Hyperdiamond

About the Vedic Square

One of the Simple Structures of Numbers that contains a lot of patterns is the Vedic Square. The Vedic Square was called the Eight Mansions in China. The Vedic Square is the Digital Root of the Multiplication Table of the numbers 1 to 9.

The Multiplication Table is a subset of the 27×27 Matrix of the 3 Triangels.

The Multiplication Table contains the Harmonics of the Numbers 1 to 9.The Vedic Square was used to build the Pyramids, create the Chinese I Ching, the Game of Chess, Dante Alighieri used it to structure his trilogy La Divina Commedia, the Sistine Chapel was build and the frescoes and symbols were arranged according to its concepts and the first chapter of Genesis was written and imbued with its numerous concepts graphic images.

File:Michelino DanteAndHisPoem.jpg

La Divina Comedia of Dante with the Tower of Babel on the background. This Ziggurat is a Geometric Structure highly related to the Vedic Square.

Scholars and Artists discovered that the various lines of the Vedic Square could be used to direct a design. By selecting a line of numbers, and using a constant angle of rotation, various designs could be produced. These designs are visible in abstract Islamic Art.

The Vedic Square is a Symmetrical Structure because AxB=BxA. This is called the Associative Property of Multiplication.  The Square is a combination of Two Triangels and contains 45 distinctive numbers.

The Vedic Square repeats itself until infinity when you extend the Square to a NxN Square.

The number pattern of the diagonal of the Vedic Square, 1,4,9,7,7,9,4,1,9,  is the Digital Root Pattern of the Square Roots. This patterns repeats itself until Infinity.

The Vedic Square contains the 5 Polar Pairs, the 8 Lo Shu Ternary Groups and the 3 Trinity Patterns ((1,4,7), (2,5,8), (3,6,9). It also contains the Star of David, The Zodiac, the Tree of Life and many other Mystic Patterns.

It is possible to transform the Vedic Square to the Lo Shu Magic Square.

The patterns of the Vedic Square Rotate. The End of a Horizontal and a Vertical Pattern connects with the Beginning of the Pattern. This means that the Vedic Square is a Torus.

This Torus is called the Rodin Torus. The Rodin Torus is a Coil that produces a Uniform Electro-Magnetic Field.

The 3-6-9 and 6-3-9 Cycle in the Vedic Square can be thought of as Clockwise and Counter-Clockwise, or as Electricity and Magnetism. They are transport-channels.

The ((3,6,9),(6,3,9)-Matrix divides the Vedic Square in 9 2×2 Squares.

The 9 2×2 Squares have a Sum of 9,18 and 27 which is 1×9,2×9 and 3×9. If we leave out the (3,6,9)-Matrix and divide by 9,  a 3×3 matrix results with 1,2,3 on the Outside  and a Cross of 2′s in the middle. This 3×3 matrix shows the Expansion of the 2 into the (1,2,3).

Patterns in the Vedic Square

The Rows and Colums of Ring Z/9 add up to 45. The Rows and Colums of the Number 3-Pattern add up to 54 which is a Mirror of 45. The (4,5)-pattern generates the Star of David and the Zodiac.

About Indian Vastu Science

The Game of Chess originated in India. It was passed on to the medieval West through the intermediary of the Persians and the Arabs.

The form of the Chess-Board corresponds to the Vastu-Mandala, the 9×9  diagram which also constitutes the basic lay-out of a temple or a city.

Hindu mythology has it that Vaastu Purusha was born of Lord Shiva’s sweat when he fought the deadly demon Andhakasura.

Vaastu Purusha himself became uncontrollable and destructive and the heavenly gods finally subjugated him and brought him down on earth with face down, with his face in the Northeast and his feet in the Southwest.

45 deities stayed there, 32 of them in the outer enclosure and 13 of them in the inner enclosure holding him in place at various points or locations on his body.

32 =64/2 and the Number of the 32 Paths of Wisdom of the oldest book of Hebrew Mysticms the Sepher Yesirah (the Book of Formation or Book of Creation, ספר יצירה).

64 is the Number of the I Tjing. 45 (5×9) is the Sum of the Lo Shu Magic Square and the Number of the Vedic Square.

All these Mystic Structures come from the same Source and are different Views on the same Pattern, the Tetraktys, the Triangular Numbers created by the Meru Prastara or Sri Yantra also known as the Pascal Triangle.

The Vastu Jain Symbol is a version of the Tetraktys

The Vastu Mandala is an expansion of  a Point (the Bindu) into the Line(2), The Trinity (3) and the Rotating (With the Clock and Against the Clock) and Expanding Square (4), represented by the Symbol of the Swastika. The Swastika is a Fractal Generating Pattern.

Every Point is a generator from which the Swastika-pattern generates a new Swastika. The 2×2 Square is transformed by the Swastika Pattern into the 4×4 and the 8×8 Square.

As you can see the Vastu Jain Symbol is an Indian Version of the Tetraktys of Pythagoras.

The Swastika contains the Four Points of the last line of the Tetraktys that are related to the Tethahedron.

About the Game of Chess

The Chess-Board symbolizes the Unfolding of Space by the Number-2-pattern and it synthesizes the Complementary Cycles of Sun and Moon.

The number 64, the sum of the Black & White (Yin/Yang) Squares on the Chess-board, is a divisor of the number 25920 (25920/64=405, 25920/9= 2880/9=320/5=72), which measures the Precession of the Equinoxes.

The Polar Pairs in the Modulo 9 Pattern are expressions of the Planets.

(1,8), the Castles, relates to the Planet Mars.

(2,7), the Bishops, relates to the Planet Venus. Venus is the Ruler of the Heart and the (2,7) is situated in the Middle of the Vedic Square.

When viewed from the Earth, the Planet Venus inscribes a near perfect five-pointed star (pentagram) around the sun every eight years. The points of a five-pointed star (pentagram) touch the circle of a pentacle every 72 degrees.  Likewise, many in Islam expect 72 virgins in heaven.

A full 360 degrees of procession takes 25,920 years, which is also seventy-two (72) 360-year cycles.

(3,6), the Knights relates to the Planet of the Messenger, Mercury. Mercury is Hermes, the Messenger God, with winged sandals. The moves of the Knights create a pattern that looks like the Swastika.

The (3,6)-number-lines are Transport-Channels (Gimel) as you can see in the Vedic Square and the Rodin Torus. The planet Mercury traces a Hexagram during its movement around the Zodiac.

(0,9) is the Planet Jupiter,  the Ruler of Modulus 9 who determinates the Rules of the Game. (0,9) is the Beginning and the End of the Game and is the cause of the Rotation of the Swastika related to the (3,6.9)-pattern.

The numbers 4 and 5 are the Moon (Queen) and the Sun (King). The Moon moves the quickest of all the planets, so does the Queen on the chessboard.

The Number 5 of the King is the Center of the 3×3 Lo Shu Magic Square and the Center of the Tetraktys.

The 8 Pawns represent  the number 2 and are connected to the Planet Saturn, the 2nd Son of the Central Sun and the Trinity (1+ 2 = 3). The Pawns start to move with 2 steps and later move 1 step. The 2 is the Center (The Son of the Sun) of the Trinity.

The 2 is also the Generator of the Expansion Pattern and the Polar Companion of the 7, the Center of the 3D-version of the Square, the Cube of Space.

The Pawn (2, Saturn) promotes into a Queen (Moon, 2×2) when he has reached the Other Side.


About the Multiplication Table of 9

About the Tetraktys

About the Trinity

About the Vedic Square

About the Tetraktys and the Lo Shu

About the Lo Shu

About the Harmonics of the Universe

About the Hyperdiamond

About the Void

About Harmonics and Entrainment

About Good and Bad Vibrations

About the number 24

About the Jitterbug of Buckminster Fuller

A Simulation of the Jitterbug Pattern (CUBIC WONDER)

About the Game of Chess

About Plato and the Sri Yantra

About the Rodin Torus

About Vastu Science

About Gematria

About Vastu Science and the Borobudur

About Programming Conversations and Conversations About Programming

Friday, July 25th, 2008

A major part of our activities have to do with “Not-Knowing”. We are constantly talking with others about “What we don’t Know”. We are speculating and are hoping that others know. Humans are wondering creatures.

The situation becomes more complicated when we meet people who are convinced they know but really don’t know. We believe them because they look like “People who know”. They are to be trusted. When we understand what they are talking about we spread the news and in due time many other people “know”.

The moment of Truth is when we Apply the Knowledge. Suddenly Everything Fails and we have to start all over again.

We are constantly talking with others about “What goes Wrong”. “What goes Wrong” is the major business of the Media Industry. What Goes Wrong is called News.

Many things that go wrong are transformed into a Reality Soap. Strange enough IT is not covered by the Reality-Soap-business.

I believe there are two reasons. The IT-business is the Most Incomprehensible Business in the World and we are accustomed to the fact “That Every Thing goes Wrong when you apply IT”.

The sad thing in IT is that a majority of the people in the IT-business don’t know what they are talking about. When a majority of Insiders is talking non-Sense the majority of the Outsiders believe they are talking Sense and are spreading the (non-)Sense to Others.

IT does not know that We (Humans) exist. IT is doing exactly what the Programmers are telling IT to do. A majority of the People in the IT-Business don’t know what Programmers are doing.

They believe they are doing something with a (programmer)language (Java, .Net) and the Internet. Some of them know important Hype terms like Web-Services and SOA (currently Agile & Blockchain!). All of them have never Applied what they are Talking about. Let’s call them Advisors.

Strangely enough the Advisors don’t understand that a Programmer is Talking to a Very Stupid Person called a Computer. The Computer is only able to do what he is Told to Do. The only thing the Advisors have to do is to Translate Human Language to Computer Language. This is a very simple Process if you know what You are Talking about.

Human Languages and Computer Languages contain Verbs and Nouns. Verbs are Processes and Nouns are States. The whole process starts with Defining What We are Talking About (The Universe of Discourse).

Many Humans are incapable to define What they Mean. They use the same Nouns in different Contexts. Some People use a Very Simple Vocabulary. Every Thing is a Thing and every Act is Doing Things.

A major part of the Activities of Advisors have to do with “not-Doing Things”. They are constantly talking with others about “What They Want to Do”. They are speculating and are hoping that IT will Solve all their Problems.

The Advisors believe that the Programmers will Understand what they are Telling and the Programmers believe that Advisors are telling them what To Do. Both of them don’t see that StoryTelling and Doing are from different Worlds. Advisors come from Venus and Programmers come from Mars.

The Users of IT Live on Earth.


I feel I am Repeating the Same Story All The Time.

Repeating the Same Story all the Time is what many people are doing but they don’t know they are repeating the same story because they use Different Words to tell the Same Story or the Same Words to tell a Different Story.

What is the problem?

The Computer needs Logic and a major part of our Conversations are not Logical at all. We are trying to find “the Logic Behind” the Conversation.

Many people are not trained to find the “Logic behind Conversations“. They believe the World is an Endless Circular Conversation.

I don’t think Believe is the Right Term. I mean they are not Aware of the Fact that they are Talking all the Time without being Aware that they are Talking. They are Programmed Conversation Machines or Machines that are producing Words that give others the Impression that they Mean something. Perhaps Words are not ment to mean something. They are just Sounds.

Many people are incapable to Apply Logical Reasoning. They don’t have the talent or are not trained in School to Apply Logic. Logic is not trained at School anymore. In “the old times” Logic was the main component of the Curriculum of the “Latin School”. At that time IT (Logic) was part of Rhetorics.

When you are Applying Logical Reasoning you are a Craftsman. When a Craftsman makes a Mistake he is really in Trouble. His Doings operate in Reality.

The Doings of an Advisor are Imaginary. When an Advisor makes a Mistake he asks another Advisor to Advice. In the End Many Advisors are Advising Many Advisors. This creates Confusion. Advisors Like Confusion. Confusion means Work and Work means Income. With “mean” I don’t mean that Work is “the same as” Confusion. I am using a Rhetoric Concept called Analogy. For some people Work becomes highly Confusing when IT (not it) is used.

When the Advisors have created a lot of Confusion the Programmers start to find the Logic behind the Confusion. When they believe they have found the Logic they create an Infrastructure to Support Networks of Confused Advisors.

This Infrastructure uses different Terms for the Same Concept to make sure that the Advisors are able To Apply What They are Talking About. This new Infrastructure supports Endless Circular Conversations and it Generates a High State of Confusion. The high state of Confusion generates lots of Work (and Income) for Advisors, Programmers AND Users.

The Advisors are Happy because they can go on with their Circular Dialogues, the Programmers are Happy because the Advisors are Happy and the Users are Happy because they have something To Do.

Perhaps Work “is a” “State” of “Being Confused“.

If we could Eliminate all the Advisors and let the Craftsman talk to the Craftsman we would Avoid a Lot of Problems.

If we would Stop Programming What is not Programmable we would Avoid even More Problems.

If we would Stop Innovating IT we could Finally start to Use IT.

If we could Program Ourselves we would not need a Computer at All.

Watch Out.

This is an Advice.


About Rhetorics

How to Analyze a Discourse

About the relationship between Creativity and Confusion

How Software Packages generate Confusion

Why Scientists are Really Artists and Why Many of Them are Creating Terrible Artifacts

Why Logic is not Logical at all

How the Programmer stopped the Dialogue

About Loops in Programs

About Software Layers

About The Rose

Sunday, October 21st, 2007

What is defensive driving and how it helps fleet managers

Defensive driving is the key mindset that will keep your fleet safe, vehicles in order and drivers in check. And it will save you and all fleet drivers the embarrassment of a typical dressing down by the interstate and highway police.

Being a mindset, defensive driving incorporates a set of driving behaviors that enables drivers achieve a daily routine that is as uneventful as possible. And that is preponderantly important in the life of a fleet manager.


What is defensive driving?

Defensive driving is a mindset that enables a motorist to identify and anticipate driving hazards. That said, it requires certain driving skills that enable the motorist to control their speed, expect the unexpected and always remain alert. It also requires respecting all drivers, as well as weather and road conditions, leveraging adjustability.

According to Wikipedia, there is a standardized way to look at it. To that end, the “Safe Practices for Motor Vehicle Operations” standard, defines it as a set of defensive driving skills, where you —the driver — are aiming to “save lives, time, and money, in spite of the conditions around you and the actions of others”.

The basic principles of defensive driving

In 1937, Mark Everard Pepys introduced the roadcraft system of car or motorcycle control. Interestingly, it’s purpose was to educate motorists on how to operate their vehicles safely. A lot has changed since this first attempt at safe driving; all for the better. Especially since the number of vehicles increased from a few thousand in the 1900s to around 1.32 billion in 2016. Without a doubt, driving safely is all the more important in 2020. To that end, certain principles were developed, to describe and support the efforts in fostering defensive driving. Get the most professional assistance from the best ny defensive driving course.

  • Always respecting the minimum and maximum speed limits
  • Being alert and distraction free at all times, so that if faced with a difficult situation you can anticipate an odd predicament and avoid the danger
  • Being respectful and pay attention to other drivers
  • Maintaining a safe distance from the preceding vehicle
  • Looking ahead, expecting the unexpected, as other motorists might not behave as you ordinarily would. This includes both motorists and pedestrians.
  • Always keeping weather and road conditions in mind, adjusting driving behavior accordingly
  • Adjusting speed before entering a bend, avoiding the need to hit the brakes in the middle of a bend.
  • Observing all driving regulations

Defensive driving: Pros and Cons

The obvious advantage of defensive driving is, of course, road safety. Today, modern fleets tend to incorporate defensive driving programs as one of the core aspects of their business. Not only is it beneficial on the road, but it brings a few business advantages, as well.


  • It’s easy to learn and adopt
  • It’s a very good way to prevent accidents
  • Leverages fuel economy and savings
  • Keeps maintenance costs as low as possible
  • Keeps insurance costs as low as possible

We have covered this subject more extensively, with 5 key defensive driving behaviors your fleet drivers need to adopt.

And, of course, there is always a flip side to the coin. Sure enough, there are a couple of cons in trying to adopt the defensive driving mindset. Undoubtedly, they’re hard to countermand, as they’re mostly related to some kind of involuntary behavior. But, it’s certainly worth the effort.