Newsletter 14: Sunday 5 April 2026

Masculinity?

“When you think back there are countless other examples to the same effect and you realize how the loss of the woman in this, the primitive story, is dealing with something which proves to have been true for man not only in the beginning, not only in the world of Greece when the gods themselves walked in the streets with common men and women and inhabited the forests and the streams and conveyed their presence and message for men through humble shepherds and mountain folk, but also today in a world where the gods have vanished into the heavens beyond the Milky Way and the whole meaning which was conveyed by a total acceptance of the reality of a creator called God is increasingly denied.  From early on I found myself wondering why I was more interested in Greek than in Roman civilisation, and the answer, in a sentence, was that at its greatest period the Greek spirit acknowledged the feminine as much as the masculine, while the Roman civilisation was entirely dominated by the man of mind, out of touch with its feminine self.  The Renaissance, for me, was precisely so significant an event in world history because in it the Greek totality of masculine and feminine, particularly its feminine inspiration, was brought back into a world dominated by its Roman inheritances.  But since the Renaissance, the caring, feeling, loving values that the feminine sense in man promotes in life have diminished, leaving only an arid, rational, masculine intellectualism and a power-obsessed urge. The moment of the container in the story, when its lid is lifted by the man and he declares it to be empty, is upon us.”

Laurens van der Post (1986) in ‘A Walk with a White Bushman’ p75

~~~~~~~~~~~~~~~~~~~~~~~~

Some Musings on Arithmetic 1

Arithmetic can be seen as an entry into Mathematics

Mathematics is the science and study of quality, structure, space, and change by seeking out patterns and formulating new conjectures, from the Greek ‘manthanein’ to learn.  One could say: Mathematics is an intelligent human response to the discovery of the wonders of existence.

At first, as a child, the world, over which the sun shines, appears to us as an outer Oneness.

We next differentiate PARTS of existence from their background, so they become separate. This requires discrimination (a process called analysis).
Once the parts are separated in our mind, we can count them, acknowledge them.

Arithmetic is the ‘art of counting’ from the Greek ‘arithmos’ number.

Numbers are not things – they are ‘ideas’.  So Arithmetic is, essentially, a thinking activity – a ‘spiritual’ science.  Most children encounter this early in their schooling.

The three soul forces of willing, feeling and thinking are involved:

• Willing.  When counting objects of a similar nature, say apples (or in a classroom, maybe, ‘beanbags’) in a basket.  One first perceives a unity, a ‘basket’.  On analysis – an important activity for a school child – the basket is seen to contain many apples.  How many?  Let’s count!  Now the activity: grasp an apple … put it on the table, and say “one” … take a second apple … put on the table beside the first one, and say “two” … and so on until no apples are left in the basket and a new pile has been formed on the table (synthesis).  The will activities incurred have been ‘grasp’, ‘put’, ‘say’. 
  

• Feeling in this situation is connected with the relationships between ‘things’ or ‘beings’, namely between the ‘numbers’ in the sequence which we learn by rote (like poetry) for counting, ‘one, two, three, four, five …’   We get to know that ‘one’ comes first; that ‘four’ comes after ‘three’ but before ‘five’.  Every language, a child of feeling, has its own set of Counting Numbers.  We know the numbers ‘by heart’.
• Thinking is a more reflective process.  Here it is concerned with the essential character of each number.  ‘One’ is all alone, I, it is lonely, so it needs to be strong and resolute.  In one sense, the whole world is ‘one’.
  ‘Two’ has a partner – they can stand side by side: II, as a pair, wings on a bird or butterfly.  Left and right hand (eye, ear, foot, etc.).  But they can also form a polarity, such as father-mother; day-night; sun-moon; up-down; forwards-backwards; window-wall; sky-earth.  Can you think of more?
  ‘Three’ can be more complex.  When three stand side by side, III, one is in the middle, with the ends being a polarity: mother-child-father; left-centre-right,  Or three, 3, can form a tripod of equals, as the three legs of a stool.  They may form a sequence: dawn-day-dusk. 

‘Four’ is the number of legs that cat, dog, cow and chair have.  Wheels on a car.  Directions: north, east, south, west.  Earth, water, air, fire.
And so on with larger numbers  – children love discovering ‘numbers’ inherent  or hidden in their environment.

*************************

 Many things connected with maths can be seen in the light of the three soul forces engaged in the early years:

• Will: creating and working with patterns and form; counting objects –   determining quantity.  Writing numbers; number operations [adding, subtracting, multiplying, dividing, etc.]; calculations.  Involving action, change.
• Feeling: rhythm and rhyme, counting sequence, relationships [equations: equals =, larger >, smaller < than]; ordinal numbers – rank, position [first, second, etc.].  Involving judgment.
• Thinking: the essence of number, symbols, concepts, cognition; qualitative aspects.  Involving imagination, picturing.

 With the names for numbers used in various European languages, it is interesting to see their similarity; perhaps the interchangeability T and D and Z when spoken.

They are all based on ten - the number of digits on our two hands. Also, 10=1+2+3+4 (sum of the first four numbers).  It is interesting that 7 (a prime number) is used in counting time: 7 days in a week - based on the 7 heavenly lights that move across the firmament of the stars [Sun, Moon, Mercury, Venus, Mars. Jupiter, Saturn.]  A human lifetime is loosely divided into 7-year epochs until the age of 63.

There are 13 weeks in a season and 4 seasons in a year, but then there are 12 months in a year.  A dozen [12] is used in packing things, like eggs.  Day and night each have 12 hours! 12 is an abundant number as it has many [4] factors: 12=2x6=3x4, while ten is a 'poor' number - it has only two: 10=2x5.

The ancient Sumerian civilisation had a base of 60.  The legacy of that is 1 hour = 60 minutes [minute means small]; and 1 minute = 60 seconds [ the hour was 'first']

Anyway, ten has been universally adopted by the modern world as the base for counting. 100=10x10;  1,000 = 10x10x10 and so on.

A more esoteric reason may be that ten has been considered of the Earth because of the four natural realms Mineral. Plant, Animal, Human as shown in this diagram where 1+2+3+4=10

When doing Arithmetic, writing the full name is rather laborious; we need a quicker system of making marks, or in some other way to keep track, to represent the number.  Historically, it has been quite a journey to arrive at the symbols used so widely today.  Let's explore:

What patterns can be made out of each number of small items - in a classroom a selection of florist's coloured glass pebbles.  Here are some - note the relation between Even and Odd -  what do you see?

Some more next week.

Robin 

Another possibility, for small numbers, is to count on one’s fingers.

If each digit (finger or thumb) represents ‘one’, then we can get to 10.

However, if we let a finger ‘f’ on our right hand represent ‘one’ and the thumb ‘t’ represent ‘five’ we can get on one hand to:  tffff = 9.

Now add the left hand where, now, the fingers ‘F’ = 10, and the thumb ‘T’ = 50, we can get to TFFFF = 90.  Both hands together give us TFFFFtffff = 99, that is:

50+10+10+10+10+5+1+1+1+1 = 99

which is nearly 10 times more than when all digits have the same value.  If every digit has a different value, then the result is ten times bigger again.  We will look at that (in an older class) when we consider the binary system, which is the basis of computer calculations.

But using our hands like this is not very convenient, as we need our hands for other things, so we need to find another way, such as making marks on something like a tablet or a sheet of paper.  Numerals have been derived from counting upwards from one:

Each row shows the symbol from the previous row with a mark added.

Each column shows symbols becoming more condensed.
Note how the Tallying result for 5 looks like a hand with the thumb laid across the fingers, which becomes the V of Roman numerals.  Then the two Vs become X (one up and the other down!)

However, the Roman numerals introduce a new element: If a smaller symbol is placed after a larger symbol (VI = 5+1 = 6), it is added;
But if it is placed in front (IV = 5-1 = 4), it is subtracted, so position becomes important.

The Western Arabic numerals, which we use worldwide today, were introduced only in the 10^th century AD, which is relatively recent.

RB

ROOM BOOKINGS