This Gnostic Book of Changes quotes Terence McKenna:
The I Ching is no magic; it is a science we don’t understand.
The 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':
The position of two hexagrams within a set of hexagrams and eight different sets add 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:
- Top 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.
The 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:
- 00 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
- 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.
Row 0 contains hexagrams 00, 01 … 07.
Row 1 contains hexagrams with octal values 10, 11 … 17.
Row 7 contains hexagrams 70, 71 … 77.
And so it goes:
a new visual order thanks to a new numerical order!
Above 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:
Posted in Concepts, General, I Ching, Number Systems, Phenomena, Polarities, Symmetries
Tagged Adobe Photoshop, Adobe Photoshop Lightroom, Article (publishing), Berkeley Software Distribution, Blender (magazine), BSD licenses, Chromebook, Computer-aided design, GIMP, Portable Document Format
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 from 0 to 7
- and hexagrams 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 first octal digit for the lower trigram under the second octal digit (upper trigram) (Photo credit: Wikipedia)
What 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
Posted in Mathematics, Science, Women
Tagged Anne-Marie Imafidon, BCSWomen, Cabinet Office, computing, engineering, gender, Margaret Wertheim, Mathematics, One Canada Square, Pythagoras' Trousers:: Physics Faith and Feminism, science, STEM, Sue Black, Technology, Women in science
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!
Posted in Image Analysis, Mathematics, Metrology, Philosophy, Science
Tagged Education, Margaret Wertheim, Math, Mathematical physics, Mathematics, Organizations, Physics, TED (conference)
Albert Einstein (Photo credit: Stoper)
According to this quotations page, Einstein wrote in Geometry and Experience in 1921:
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
It’s been a while that I discovered how metrology is the missing link that Einstein was looking for. But not with its uncertainties and probabilities due to the current mathematics implemented to quantify physical, chemical and other measuring units, as I am introducing pixel accuracy.
- Current mathematics is based on ‘paper thinking’, i.e. static writing.
- My qualitative metrology stems from ‘software aided thinking’, i.e. dynamic coding.
3D metrology is based on new mathematical spaces and transformations that have to be expressed through code. Continue reading
Last night, I attended an event at the Royal Institution about Penrose Tiling – the wonderfully aesthetic effects of joining basic geometric shapes and studying their behaviours towards infinity.
I thought of ‘where algebra, geometry and number theory don’t meet’ and felt nicely re-assured in my understanding.
But during my Yoga class earlier in the day I had thought about time, space and measuring.
For measuring is more than comparing.
Posted in Algebra, Arithmetic(s), Geometry, Mathematics, Measuring, Metrics, Metrology, Number Theory, Philosophy
Tagged Giordano Bruno, Measurement, Number theory, Penrose Tiling, Physics, Roger Penrose, Royal Institution, Space