Category Archives: Geometry

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.

Continue reading

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.