Category Archives: Mathematics

Bruno, Bach and Pythagoras: architects of light, sound and number

My mum (1922 – 2011) who understood me better than anybody else gave me the book Gödel, Escher, Bach by Douglas Hofstadter (1954 – ) ages ago.

But my most likeminded heroes must be Giordano Bruno (1548 – 1600), Johann Sebastian Bach (1685 – 1750) and Pythagoras (570 BC – 495 BC) – besides everybody who contributed to the evolution of computing.

These Golden Verses are attributed to Pythagoras and end with:

  • and Thou Thyself Shalt by Thine God in one translation I read.

Pythagoras is famous for his theorem a2 + b2 = c2. But what I have put into software is his other famous saying:

  • All is Number – the subject of a cute 6-min Chinese video which also makes the link to BELIEFS and religion.

I found my favourite quote of Giordano Bruno in the Museum for Telecommunications in Berlin:

  • There is no time. There is only movement. For if there was no movement, there would be no time.

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Numbers in the Old Testament

When updating my last post about the Digital I Ching, WordPress showed me 25 quotes by Terence McKenna that will blow your mind published by The Unbounded Spirit. I found them inspiring and insightful, especially the link between Cult and Culture, given that we are dealing with a father whose children accuse him of being the leader of a cult that kills babies and abuses them and 18 other ‘special’ children…

I also stumbled into NUMBERS as the fourth book of the Old Testament. There are 35 chapters in NUMBERS. Reading just the titles, is like reading the history of people divided between living in unison with god and fighting that what can be called god or ‘universal’ and ‘cosmic intelligence’.

I noticed the ‘threescore’ for Judah and Dan. I wrote it as if it meant 100,000, but that’s hardly correct. The ‘numbering by their names’ is to me the attribution of numerical values of letters.

  1. The Numbering of Israel in Sinai
    1. The tribe of Reuben: 46,500 were ‘numbered by their names’ who were able to go forth to war;
    2. Simeon: 59,300
    3. Gad: 45,650
    4. Judah: 314,600
    5. Issachar: 54,400
    6. Zebulun: 57,400
    7. Ephraim: 40,500
    8. Manasseh, 32,200
    9. Benjamin: 35,400
    10. Dan: 302,700
    11. Asher: 41,500
    12. Naphtali: 53,400
    13. The Levites were not numbered, but ‘appointed over the tabernacle of testimony’.
  2. The Camps and Leaders of the Tribes
  3. The Number and Duty of the Levites
  4. The Tasks Assigned to the Levites
  5. The Unclean Driven from the Camp
  6. The Law for the Nazarite
  7. Offerings for the Dedication of the Altar
  8. Aaron Lights the Lamps
  9. The Observance of the Passover
  10. The Silver Trumpets
  11. The LORD Sends Quails
  12. Miriam and Aaron Speak against Moses
  13. The Twelve Spies Sent to Canaan
  14. The People Rebel against the LORD
  15. Laws concerning Offerings
  16. Korah’s Rebellion
  17. Aaron’s Rod
  18. Provision for the Priests and Levites
  19. The Purification of the Unclean
  20. Water from the Rock
  21. The Canaanites Attack Israel
  22. Balak Sends for Balaam
  23. Balaam Blesses Israel
  24. Balaam’s Prophecy
  25. Israel Worships Baal-peor
  26. The Numbering of Israel in Moab
  27. The Request of Zelophehad’s Daughters
  28. The Daily Offerings
  29. The Offerings at the Appointed Feasts
  30. The Law concerning Vows
  31. Israel Takes Vengeance on Midian
  32. Reuben, Gad, and Half of Manasseh Settle East of the Jordan
  33. The Stages of Israel’s Journey
  34. The Borders and Division of Canaan
  35. The Inheritance of the Levites
  36. The Law concerning the Marriage of Heiresses

In our troubled times, we each have to find our sources for meaning and making sense of all phenomena around us.

Blessed be the internet with its fountains of data, information, knowledge and wisdom!

DIGITAL #ICHING: new #Patterns, #Designs and a new #Science thanks to Octal Numbers

This Gnostic Book of Changes quotes Terence McKenna:

The I Ching is no magic; it is a science we don’t understand.

t-shirtThe science that I am offering, comprises a new understanding of

The use of octal numbers has allowed me to find ‘stable’ hexagrams, i.e. those with dual octal digits: the values 00, 11, 22, 33, 44, 55, 66, 77. 

In digital designs, they can be represented from four ‘view points’ or ‘cornerstones’:

When used for divination, two hexagrams are used: one to represent the Here and Now and a second one that the current situation changes into, based on those lines that change when we make our conventional or binary divination.

The position of two hexagrams within a set of hexagrams and eight different sets adds new scope for interpretation:

1. Which ‘quadrant’ or ‘directional context’ of change do our two hexagrams occupy? That depends on the ‘intensity’ of change, as indicated by the ‘stability’ of the two hexagrams:

  • Stable UnstableTop Right, if both are stable;
  • Top Left, if the first is stable and the second one unstable;
  • Bottom Left, if both are unstable;
  • Bottom Right, if the first is unstable and the second one is stable.

P F U CThe meaning of the quadrant position is explained also under polarities:

  • the Left is the Past and the Right is the Future
  • the Top is Consciousness and the Bottom is Unconsciousness.

2. Which ‘plane’ are we moving from and to:

  •  4 Quadrants 00 7700 or Dark (Earth, night) to 77 or Light (Heaven, day):
  • becoming conscious of ourselves and our world – as on the left – if the first hexagram is < or smaller than the second one;
  • here the four ‘quadrants’ are home to complete sets of hexagrams – showing fourfold symmetry – both visually and numerically.

It is this combination of visual beauty and numerical accuracy that adds new value to this ancient wisdom.

Or are we moving

4 Quadrants 77 00

  • 77 or Light (Heaven) to 00 Dark (Earth):
  • becoming inspired by the Universe – as on the left – if the first hexagram is > or greater than the second one.

3. How do we interpret the comparisons of visual positions and numerical values of two hexagrams?

  • Stable hexagrams in diagonals illustrate directions of change: between Light (day) and Dark (night).
  • Quadrants of single sets of hexagrams bridge polarities of time: past and future as well as awareness: unconscious and consciousness.
  • Planes of four sets of hexagrams bridge polarities of space: Heaven and Earth as boundaries for humans: inspiration and manifestation.

Related articles

DIGITAL #ICHING Hexagrams in new Visual Order thanks to Octal Numbers

Matrix with Grid and NumbersRow 0 contains hexagrams 00, 0107.

Row 1 contains hexagrams with octal values 10, 1117.

Row 7 contains hexagrams 70, 7177.

And so it goes:

a new visual order thanks to a new numerical order!

1 00 77Above all, marvel at the beauty of the visual and numerical symmetries!

These are the first images I produced with GIMP.

I can’t use more than 3 colours if I also want to use the visual diagrams as digital designs on t-shirts and other accessories.

Let’s see where the digital paintbrush will lead me…

In the next collection of diagrams you will notice the symmetry created by organising the hexagrams in four different ways:

  • from four ‘corner stones’ or ‘zero point’ positions.

Thus they form a new kind of ‘visual ensemble’:

Light (heaven) at the centre radiates towards Dark (earth) on the outskirts.

And now in reverse order, with earth at the centre and light at the periphery:

Or with the highlights of colour:

1. from 00 to 77, i.e. Earth to Heaven, starting at four different corner points:

2. from 77 to 00, i.e. Light or Heaven to Darkness or Earth:

More on:

Related articles

DIGITAL #ICHING: Octal Numbers as new Ordering Principle & 8 as Chinese lucky number

I wish I could remember what made me

Funky Facts about 8

think of what now is so obvious: the use of octal numbers to re-order the hexagrams 1 to 64 (base 10) from 00 to 77 (base 8), leading to remarkable visual effects.

So I used

  • trigrams numbered from 0 to 7
  • and hexagrams counted from 1 to 64
  • to renumber them from 00 to 77

and produced a lot of

Hence I was amused to discover that for the Chinese, the New Year is the Year of the Sheep, starting 19 February, with the number 8, considered to be the luckiest number, being ubiquitous, as said on this site.

I Ching hexagrams 00 to 77 with: left the firs...

I Ching hexagrams 00 to 77 with: left the first octal digit for the lower trigram under the second octal digit (upper trigram) (Photo credit: Wikipedia)

TOWARDS a Gender-Balanced Agenda: with #WomenShiftDigital, #techmums, #savvify + Smart Knowledge Portals?

13 11 27 PythagorasWhat a day: Women Shift Digital!

What a venue and sponsor: Level 39 in One Canada Square.

And what a fantastic quantity of quality women – starting with

I THINK – aided by software – therefore I AM: Mathematical Woman, here I come!

Scottsdale Coral Reef project

Scottsdale Coral Reef project (Photo credit: crochetgal)

It may sound terribly presumptuous, especially for the English culture, when I write: Mathematical Woman, here I come. But I am old enough to wear a Purple Hat with pride and am just reading God, Physics and the Gender War.

The author Margaret Wertheim writes beautifully about science and the problems that it hasn’t solved yet – also in this TED discussion. And she writes about the Ascent of Mathematical Woman, besides all the reasons why women haven’t had equal chances yet. At the last event on Intelligent Imaging we were 64 participants and 4 women.

Her chapter on Rene Descartes who is famous for “I think, therefore I am“, reminded me of what I always claim: by practising ‘software-aided thinking’, I re-visited mathematics through the eyes of a mature programmer and came up not only with incredible insights, but also prototype software that produces unique screenshots by demonstrating three innovative software methods.

If men can be humble enough to express their admiration, I get a bit of positive body language. The professor who said “This is the most important work since relativity theory, because it’s about understanding number” claimed later I was mis-quoting him.

So I keep trying to find potential clients, collaborators and partners with whom to build smart knowledge portals without explaining the mathematics behind them.

Let the software drive the minds of its users
as an engine moves the car of its drivers:
without knowing how it works.

But humans want to know how things work around them:
the light that wakes them
the dark that puts them to sleep
the strong that holds them together
and the weak that lets things fall apart…

May Mathematical and Data Women repair
what has fallen apart in the past!