Category Archives: Mathematics

TIME, Space and Measuring – on the quantifications of 2D and 3D worlds

Oil painting by Urs Schmid (1995) of a Penrose...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.

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THE Photonic Ocean of Light

English: The Archimedean spiral

English: The Archimedean spiral (Photo credit: Wikipedia)

Light Energy in Photons, Orbitals and Spirals


If there is a beginning, there is Light Energy.
Measured in photons in motion and phonons in stillness.


A spherical photon comes from the photonic ocean of a sun.
When Light Energy moves, it follows spiralling pathways of motion.
Spiralling pathways are orbitals: the cycle or turn of a spiral.


In stillness, many orbitals form one spiral.
Their pathways are light threads.
Their density determines brightness.


In motion, spirals are dynamic:
two-way motion
along orbitals in 3D Space
creates alternation.


Alternating orbitals create pulsation in terms of linear movement:
between an upper and a lower spiral,
the two halves of a double spiral.


Alternating orbitals also create a dual shape: a cone and a pyramid,
in terms of 3D Motion Shape,
with centripetal and centrifugal effects of spiral motion.


And in addition to photons on orbitals, in conic and pyramidal spiral shapes,
there is the right/left dynamic of intertwining spiral twins.


Light energy in spiral twins is spinning:
charging and discharging, raising and lowering potential.


Circular right/left spin and vertical up/down pulsation,
these determine the spiral’s charge,
its electric potential:
an amplitude and a frequency
in spiralling terms.


But space has three dimensions.
Two-way dynamics resonate in three-way fields.


The spinning spiral twins pulsating in dual spiral shape,
create wave fields of light in spherical shapes.


In dark, cold and vast space, spherical wave fields of light radiate and are reflected:
spherically by their own boundaries and orthogonally by opposite space conditions.


Dynamic 2-way motion creates 3-way wave fields.
Thus we need to study harmonic 3D resonance that result from dynamic 2-way motion.


Opposite light energy conditions meet opposite space matter conditions.


Balance is naturally and lawfully redressed with respect to
 the quality of light
 the characteristics of energy
 the shape of space
 and the form of matter.


NUMBERS in Arithmetic(s)

English: Multiplication is often taught as rep...

If you add and subtract,
0 is nothing.
If you advance forward or backward,
0 gets you nowhere.

But when you begin to multiply,
you annul and annihilate
by associating with 0 as one of your factors.

Yet what is multiplication
if not compounding addition?
Adding a bunch at a time
not just One.

Anything + zero is anything.
But anything * zero is nothing.

Yet, geometrically speaking,
multiplying means going in two directions:
so many steps by factor 1
and, at right angle, so many steps of factor 2.

Unitary steps along an axis
become unitary squares in the plane created by co-ordinates.

However, + and – are a quality as well as an operation.
As a quality of number they mean right ® or left: ¬.
As an operation on value, add or subtract.

Positive and negative is only one aspect of + and –
when they describe the quality of constants.
Right and left is another one:
inherent in numbers,
noticeable as orientation for spin and motion.

Constants are solid numbers.
Their value is fixed.

But 0 and 1 are special constants,
for they have special value:
in the creation of centres of balance and gravity,
units of duality and polarity and symmetric twins of change and motion,
as building blocks
for all else to follow as opposite and polar pairs:
direction, operation, transformation.

FROM Constants to Variables

Logical connectives

Logical connectives (Photo credit: Cuito Cuanavale)

In their infinity of appearance,
numbers can be clothed in the generality and variability of letters.

Then their difference in value is hushed over, covered up.
Except in those languages
where letters and numerals do have the same value – as it was in Ancient Greece!

All this is fine and it all works.
It has worked to get people to the moon
and rockets into space.

But for earthlings to become cosmic,
they need to become fuller of care, more care-ful:
more distinctive and distinguishing
between 0, 1, 2, 3
and other numbers.

Generalising 0, 1, 2 and 3
is not appropriate.

0, 1 and 2 are cosmic prime numbers,
divine constants,
the ones from which all else springs.

Their generalisation consists in the rules by which they function,
the laws by which they abide, the principles that they generate.

Their functions can not be generalised.

They are unique and primary,
primordial and original.

Algebra is generalisation:
from constants to letters.

Geometry is visual representation:
of static constructs and dynamic functions.

But the visual of a generalisation
is more than geometry:
it is art and cosmology,
intuition and creation.

The geometry of algebra
is different
from the geometry of numbers.

Pythagoras taught whole numbers in geometric shapes.
Mathematicians today use variables in geometric co-ordinates.

Mathematicians are logicians:
they think logically.

They apply rules like a computer.

And as a mathematician
I say to thee:
The Universe is logical, too.

It is consistent in space and continuous in time.

Its logic is so deep and so simple
that our thoughts need to stop
for our mind to grasp it.

It takes the mind to want to know,
and the eyes to want to see.

And it takes consistency of thinking
and the rules of logic
to follow its magic.

I hope I have made it clear –
what I see and have seen,
what I think and have thought.

May it help you on your journey
of understanding its essence and fundamentals,
its logic and magic.

The Cosmic Prime Numbers 0, 1 and 2
deserve regal treatment.

They merit divine adoration
and masterly operations.

For mathematical operations
are to numbers and variables
what medical treatments are to patients
and emotional communications for partners:
causal processes resulting in effects.

Treat them gently, the cosmic numbers 0, 1 and 2,
don’t think they are so alike
that they can be described as n.

Treat them depending on their context,
of position and function,
of space and in time,
and always in absolute 3D.

Watch out for the absoluteness of 0,
that creates the relativity of 1,
the unit of polarities that 1 creates
and what pairs of symmetry 2 is producing.

Don’t line them up,
don’t use them to flatten the earth,
don’t unify them
in the desire for your unity.

COSMIC Constants as Universal Principles

The Thinking Man sculpture at Musée Rodin in Paris

The Thinking Man sculpture at Musée Rodin in Paris (Photo credit: Wikipedia)

 Thesis, antithesis and synthesis are noble principles
for learning and comprehending.

In Western thinking, analysis or dissection comes first.
Synthesis or wholeness is what we are striving for.

Synthetic are those operations that are building and augmenting: addition and multiplication.

Analytical are those that are reducing and diminishing:
subtraction and division,
creating fractions and negativity, roots and complexity.

Putting operations in 3D, means operating either above board
or below the x/y plane of z=0.

Perception and observation lead to abstraction and generalisation.
But the hardest of all are conceptualisation and universalisation:
to find concepts that reflect the greatest common denominator,
and formulate them such that they are true, universally.

To go deep enough to see universal truth,
to think long enough to know cosmic law,
may take meditative stillness
and focused concentration.

Over millennia, humanity has observed and abstracted,
generalised and universalised,
focused and concentrated.

It seems to take evolutionary ideas and synchronistic thoughts
to produce newness:
thinking in rhythm with the cosmos,
in the timing of the universe.

And it takes computers to help our thinking along:
as a reflective mirror,
a responsive drawing pad,
an interactive pencil
and a looking glass with a difference.

Abstraction in thought means finding higher levels of commonality:
the common multiples,
where ideas meet and come together.

In calculus, higher levels
are found through the process of integration,
with results of 0 and ¥.

In algebra, abstraction means generalisation.
Generalising means substituting numbers with n
where n can assume values from 0 to ±¥.

Constants are numbers, the bedrock of mathematics.
But 0 and 1 are more than constants.

0 and 1 are cause and effect,
law and principle,
builders of numbers,
architects of constants
motors of all movement.

Numbers have value (cm, pounds, £) and no value (0, 1, 2, 3).
Constant or variable, value and none.
In cosmos and nature, they are and they make happen by their very being.

Whether they are observed or not, valued or not, by humans and mathematicians.

Just as a brick has value by being in a wall,
numbers don’t need a price tag for existence.

Ownership does NOT give them their raison d’être.
They have value by being.

At the right time, in the right place: Zero as a centre of balance,
with the right distance to determine One as a unit for reference,
so that 0 and 1 create the God-given twin symmetry for completion.

2 is the higher level for 0 and 1: the first level of integration.

THE Eternal Process of Creation

Speed of light (Fizeau)

Speed of light (Fizeau) (Photo credit: Wikipedia)

Rotating around our still point and pole,
circulating in an orbit of gravity,
and integrating the push away and the pull towards,
this is stillness in motion,
meditation in action,
energy transforming into matter
to find form through fields
and back.

The eternal process
of creation of visible matter
from invisible energy,
and order of relative motion
from objects in absolute positions –
both inside our mind and outside
is unending a dance –
of life outside and exploration inside.

When e = mc2,
c2 is the attempt
to describe the powers
that create form.

Form for matter.

The speed of light
is measured
as linear distance
and squared.

What if we measured the length of a sin wave travelled?

 The circumference of a sphere
unravelled as wave
along which light particles rotate
on their seeming journey to earth?

God creates numbers and units
and One as measure.

Who am I to establish a measure
for the speed of light?

Just a new way of looking:
from lines to waves,
from a straight distance
to a curved sin wave.

FROM One to Two: another Quantum Leap?

English: Vortex with autumn leaves Cayte Made ...

English: Vortex with autumn leaves Cayte Made with GIMP and Inkscape (Photo credit: Wikipedia)

From the radius of a circle of One,
comes the diameter of Two:
of a sphere
that contains all:
and spiral turns,
rotating in its own vortex of energy
moving in suspension along an orbit
that is defined by a larger sphere.

But definition is not evolution.
God did not sit and define.
God put into motion
and watches evolution.

By creating One
God created Two
as perfect symmetry,
complete polarity
or imperfect duality.

There is no subject and object.
There is only One and the first
and evolution that makes the next follow.

In god’s wisdom,
the second was symmetrical.

On as many levels
as One is multi-functional.

And all symmetries and polarities
can be united and transcended
in a third dimension.

Two spheres resonating,
two vortices inter-relating,
two fields inter-acting,
two masses inter-attracting,
two orbits inter-twining,
two movements inter-connecting,
result in a third: the Big InterChange.

Symmetries of two
moving in three-dimensional space –
this is the model for life:
for man and woman on earth
and planet earth in space,
for god and humans in Cosmos.

My prosaic life gets blogged on and