Newsletter 30: Friday 24 July 2026

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The Foundation Stone text contains references to the Hierarchies.  They are listed as

First Hierarchy:-  Seraphim, Cherubin, Thrones.

Second Hierarchy:- Kyriotetes, Dynamis, Exusiai.

Thirda Hierarchy:- Archai, Archangels, Angels.

It is very difficult to comprehend even the very least of these beings from everyday experience.  We have to rely on Rudolf Steiner and Anthroposophy for descriptions of any kind.  In fact, the greatest of these, the Seraphim are so mighty that anyone granted a glimpse of them unprepared would go mad.  The task of the “Guardian of the Threshold” is to protect us from any possible glimpse of the beings of the spiritual world that could be harmful to us.

 Even so it is possible to form concepts that allow us to imagine who these beings are. Sergei Prokofieff, in “The Foundation Stone Meditation”, in the second chapter, gives a characterisation.  He characterises the third hierarchy as beings of truth.

The second hierarchy are creative beings who create, but whose creations are not able to become independent.  The first hierarchy can create and whose creations can continue in an independent existence. 

 Perhaps it is more helpful to characterise them in a way that relates them to human experience. 

Angels can offer person to person guidance...  individual guidance.
Archangels guide communities.  Where people combine in communities, Archangels can be involved. 
Archai are “Time Spirits”.  The give guidance to an age, a period of time in human history.

It is more difficult to conceptualise the second hierarchy and their activity.  First, they are not so directly involved in human affairs, but they do have an influence.  For instance, Exusiai, as “Spirits of Form” have a relationship with any creation that has form, that is it is made of a material that can take shape or form.  So naturally, that includes all ‘embodied’ creatures....  creatures with bodies.

The Dynamis, or “Spirits of Movement” are connected to any creation that is able to move.  That would be any animal, but also water and air. 
The Kyriotetes are also called “Spirits of Wisdom”, which implies they have a connection with any creation that has wisdom  secreted into its existence.  So ......  everything?

 What about the First Hierarchy.  These are beings so exalted that human words are rather inadequate to describe them and their activity.  So, bear with me as I stammer some totally inadequate words to this effect.

 The Seraphim are the highest.  They are beings of WARMTH.  This warmth is so great that, in comparison, the sun is just a candle. They are connected in some magical way with the human heart realm. 

The Cherubim are next.  They are beings of LIGHT.  All the light of the world emanates originally from them.  Space is filled with light. We see out into space at night and we see dark.  We are in the earth’s shadow.  The earth is the darkest place in existence.  When we are out in space we are illuminated by the sun and the stars.   Rudolf Steiner’s characterisation of the sun, is that it is a being that reflects the light streaming in from around us, from the far, far, depths of space.  If you have difficulty with this idea, so do I, but it is an exercise in keeping an open mind. 
The Cherubim are connected with the human head and nervous system.

The Thrones are the Will beings of the First Hierarchy.  Will is very difficult to comprehend as the will proceeds in essence, from beneath our usual consciousness.  So, for this reason, it is difficult to form concepts of the activity of the Thrones.  They are the beings, who, in the beginning of all existence, poured out their will substance into the “space” created by the Seraphim and occupied by the Cherubim.    

The Beings of the Hierarchies, as listed in the Foundation Stone Meditation, number nine:-

1st: Seraphim, Cherubim, Thrones,

2nd: Kyriotetes, Dynamis, Exusiai,

3rd: Archai, Archangels, Angels.

 Human beings are tenth as a start to a 4th Hierarchy level.  Development will continue beyond Earth existence, however, and on the coming Jupiter evolution, there will be new beings who exist on the “human” level of existence.

 For our everyday thinking there is little that can help us to form a picture of the nature of these beings.  If you think of an angel as a being with wings, bending over us, whispering helpful advice in our ears when we need it, is about the closest that our modern life can give us to the true nature of the angels.  However, they are much more magnificent that this.  The bible story in the gospel of Luke, of the shepherds in the fields, surrounded by a heavenly host of angels singing, is somewhat closer to a picture of them to comprehend the truth of their existence.  Rudolf Steiner gives us some further glimpses into their true nature throughout his lectures to members.  The best description that I have read, and can locate, is in Occult Science, where he describes the evolution of the Cosmos.  He describes the coming into being of “Saturn”.  There is, first of all, the work that Seraphim, Cherubim and Thrones carry out in bringing about the existence of something OUTSIDE of the Spirit World of these three great Cosmic beings.

The next existence after the Saturn existence is called the “Sun” existence.  This is brought into existence by three Higher powers:- Cherubim, Thrones and Kyriotetes.  All one degree lower than the progenitors of ‘Saturn’.  In this existence air is brought into existence in addition to warmth.

The third evolutionary stage of our cosmos is called the “Moon” evolution.  The progenitors of this cosmos are Thrones, Kyriotetes and Dynamis.  Here, water comes into existence.  So, on ancient Moon, there is Warmth, Air and Water.

Our present fourth existence comes “Earth” comes into being under the Kyriotetes, Dynamis and Exusiai.  In other words, it is the creation of beings entirely from the Second Hierarchy.  A fourth condition starts its existence in this stage of evolution, the solid condition!

It is interesting to reflect here on some comparisons.  The Saturn condition is made entirely of warmth and is initiated from the Seraphim, who are essentially fire beings.  The Seraphim and Cherubim [who are essentially beings of light] give rise to the “space” in which the Thrones pour substance….  that of warmth.  This substance has will character as the Thrones are beings of will. 

I struggled with this idea for a long time.  However, I got some help with a description in a lecture by Georg Hartmann, where he characterizes this as “condensed will” as like will “sweated” out.

The second evolution, the Sun evolution, is initiated by Cherubim, beings of light.  .

The third evolution is the Moon evolution, a water evolution.  A will evolution, initiated by the thrones.  Think of this. Water will NEVER, EVER stop trying to get to the sea.  That is the picture of the strongest kind of will.  It never gives up.  Never.

 I loved the stories of the Kalevala that my mother read to us when we were children.  On the Kalevala is a hero named Vainamoinen.  He sings the world into existence.  In his further adventures he is able to bring about magic through singing. This picture lived strongly in my childhood imagination.  It was a help when, as a teacher of chemistry, I struggle to comprehend the table of the elements.  For many years I lived with this riddle, not knowing what to make of this table, when Rudolf Steiner, in Anthroposophy, gives us FOUR elements.  However, repeated efforts to sort it all out led me to this.  In Fire of Saturn there is only hot and cold, and varying degrees of these.  On ancient Sun there is air;-  thin air,  thick air, warm air and cold air.  On     ancient moon there is water, airy water, bubbles, steam, hot water, cold water but not any ice. Only on earth there is there a multiplicity. 

 Here, in the solid condition, we find all the other elements.  Calcium and iron, lithium and boron, sodium and chlorine all have their existence in the solid condition.  But there still remains the riddle of their true existence.  Scientists insist on a fable of nucleus, electron shells and the like, but never, at any point does all this theory give rise to the secret of the distinctive CHARACTER of the individual elements themselves. Iron, Scandium, Titanium, Vanadium, Chromium, all for example have similar electron configurations, with just a small change of one further electron.  The character of the metals is Oh! So different. 

 At this point, Vainamoinen came to my help with an imagination.  I imagined a whole choir of brothers of Vainamoinen,  standing assembled into a choir, each singing a different element into existence.  Each element with the character of the hero singing it into existence.  I have lived with this picture for a long time now.  It still holds water.  It has validity. So, I imagine the choir of the Exusiai, the Beings of Form, singing into existence the characters that become the substances of the solid earth.  

Christopher Bacchus

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Arithmetic Musings #17

Growth by multiplication. 

In Maths there several levels of intensity in the processes that expand or grow Number:

1. Counting upwards: 1, 2, 3, 4, ....
2. Addition: putting one pile on top of another: 3 + 5 = 8
3. Multiplication: creating an area: 3 * 5 = 15
4. Exponentiation: raising a base number to a power: (binary) 2¹⁰ = 1,024; (decimal) 10³ = 1,000 [kilo]. From Geometry we get the terms: square from 2*2 = 2² = 4, and cube from 2*2*2 = 2³ = 8 
5. Integral Calculus: used to find the area under a curved line, or the sum of a series of numbers.  
   We can perhaps get a picture 4 aspects of physical motion: distance travelled, d; time taken, t; speed or velocity of the vehicle, u initial speed, v final speed, the distance travelled every second; and the acceleration/deceleration (braking) causing change of speed during the journey, a.

Sir Isaac Newton devised equations of motion for steady acceleration, as when an object falls down under the influence of gravity:

Increase in speed: v-u = a*t; or  v=u + a*t
Average speed: (u+v)/2
Distance travelled: d = t*(u+v)/2 = t*(u+u+a*t)/2 = u*t + a*t²/2

Calculus deals with more complicated situations when acceleration and braking is continally changing (eg. a racecourse)

There appears to be no upper limit to the size of numbers, or perhaps we should say it is 'undefined'.  The term used for the largest number is Infinity. (without end, no finish)

It is interesting that the reverse processes that diminish or contract numbers reach thresholds, and a new type of number is born, but you need to be attentive to notice it rather than ignore it.

1. Counting downwards:  ....5, 4, 3, 2, 1, 0   zero, nothing, zilch, empty.  A new idea - but why be interested in nothing, haven't you got something to do?
2. Subtraction: 3 - 5 = -2,  Here there is confusion because the same symbol is used for quite different purposes: first as 'minus', a symbol for the operation/activity of subtraction; the second as a symbol for 'negative', an adjective for a number positioned below zero in the number line. There is a whole world behind the mirror of 'zero'.  ("Alice through the Looking Glass" was written by a mathematician.)
3. Division: [rationalising] 3 ÷ 5 = 3/5. ' three-fifths', a fraction, a broken number.  Now there is an 'infinity' of numbers just between 0 and 1.  Here the relationship between the two numbers is important.  Sometimes this is expressed as a 'ratio' 3:5  (the ratio of 3 to 5).  This leads to another name for them as "Rational Numbers", implying that they are 'thinkable' numbers. [as long as it doesn't give you a headache!]  More likely: when sharing a dividend among several people, each gets a ration.
4. Extracting roots:  The number, which when squared gives 4 is the square root of 4, namely 2.  Similarly, the number, which when cubed gives 1,000 is the cubic root 1,000, namely 10.  The symbol for this process is √.  So, 2 = √4; and 10 = ³√1,000.  In this case, the answers are integers (whole numbers).  However, there are many numbers for which there is no rational number that works.  Consider 2.  What is √2?
   
   

Guess:  let's try a first guess, a,  for √2 of a = 3/2.  Then a² = 3/2 * 3/2 = 9/4 >2, obviously too big by 1/4.
 Let's try a second guess (a little smaller), b  = 10/7.  Then b² = 10/7 * 10/7 = 100/49 >2, only too big by 2/49.  (Next guess, c = 100/71) 
No matter how hard we try, we cannot find a ratio that works exactly.  Perfection is not possible!
So, √2 is called irrational, literally 'unthinkable' or without reason.  Another name is 'surd', - you can see the relation to absurd.  Actually, surd means deaf or mute, speechless, without a voice.  At best we can find a decimal approximation for these roots - a topic for a future musing.

        5.  Differential Calculus: used to find the slope or gradient of a line - expressed as the ratio of the change in height to the change of distance between two points on the line.  To express the changing slope more accurately the points need to be drawn closer together, until they are almost touching! In the limit they become infinitely small or infinitesimal.  The new concept here is the "limit" approaching zero.

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 If you have any comments or requests, please feel free to contact me.  RB  robin@bacchus.co.nz