Chapter 17: Perspectives (1)


The two chapters entitled 'Perspectives' are likely the most radical of this book; if you can properly understanding these two chapters then you should have a good feel for 'where I am coming from'. Many of these perspectives were not included in earlier drafts of the book, since I felt that my relative lack of insight made me unqualified for the task. I still feel unqualified - a great deal is only intuitive, but at the limits of my awareness, the truth of what is written grows stronger.

When contemplating the future evolution of spiritual expressions on Earth, two images have frequently come to mind. They make use of maritime analogies:
Suppose you are keen to cross a stormy sea. You have before you a raft and a large boat, both as good as new. What do you decide for your course of action?

Now suppose that you wish to rescue some people who have been thrown overboard in a storm at sea. They can swim, but are being carried quickly away by powerful currents. To save them with your life-boat you cannot ignore the currents!

How a problem can have direct and indirect solutions

The purpose of the following example is to intimate how valid methods for solving problems can differ quite considerably. The title expresses a mathematical problem in its general form, of which the text that follows is just a special case.

Example: Counting subsets of a given finite set

Suppose we have a box of 3 cuddly toys (an Elephant, a Teddy Bear and a Panda). We would like to know the number of ways of choosing different combinations of the toys for some children to play with. If the children are well behaved then we might empty the box, i.e. choose all 3 toys - one combination; or, if they have misbehaved, we might leave the box untouched, i.e. choose 0 toys - another combination.

So how many different combinations are there?

Solution 1: 'direct' approach

We determine in turn the total number of combinations for selecting 0,1,2 and, finally, 3 toys. This yields:-

Number chosen Combination(s) No. Combinations
0 No toys 1
1 Elephant; Bear; Panda 3
2 Elephant & Bear; Elephant & Panda;
Bear & Panda
3 Elephant, Bear & Panda 1

Total number of combinations = 1 + 3 + 3 + 1 = 8.

Solution 2: 'indirect' approach

We consider each toy in turn. Either the toy is picked or it is not, i.e. there are 2 options per toy. By doing this for all the toys we can derive exactly the number of combinations:-
          Bear           Elephant            Panda
     1.   Yes              Yes                Yes
     2.   Yes              Yes                No
     3.   Yes              No                 Yes
     4.   Yes              No                 No
     5.   No               Yes                Yes
     6.   No               Yes                No
     7.   No               No                 Yes
     8.   No               No                 No
As each toy is picked independently of the others, the number of combinations is the product of the number of options for each toy, i.e. 2 * 2 * 2 = 23 = 8.

In general, given n toys in the box, there are 2n different combinations of toys which may be chosen. For large values of n, the second method is evidently quicker in the evaluation of the total number. The key to an easier solution was the finding of an alternative characterisation of the original problem.

Tentative applications to the issue of effective treatment of mind

The psyche (or conditioned mind) is not the spirit (or unconditioned mind). Talk is often overwhelmingly of the need to realise our spirituality in rather an idealistic fashion. Eventually, we face, however, the question, 'What method(s) do we choose?' What treatment do we take for our injured mind's eye? Whatever the treatment chosen, its prescription is initially defined within the conditioned environment, albeit for some perhaps in layers of mind far subtler than corporeality.

For there to be recognisable benefits, there need not be any reference to lofty spirituality. The 'patient' should be mindful of just dutifully accepting and taking the treatment. If the patient benefits as a result without adverse side effects then the method has been seen to work. What is crucial here is that whoever oversees the administering of the prescriptions is spiritually awakened and knows what outcomes are likely (which usually means: has taken such treatment himself/herself). This all sounds mundane, but it is wholly consistent with, for example, the notion that genius is 10% inspiration and 90% perspiration. Keep applying the treatment and sooner or later the breakthrough is made and there is spiritual transformation.

Someone who is concerned for the spiritual well-being of people can thus shift the view from lofty goals to effective treatments. It is well known that many people approach meditation for only practical reasons and then at some stage they suddenly break through into spiritual aspects. Meditation is thus an effective treatment.

Those who have undergone or who practice (Western) psychotherapy may have had similar experiences. Psychotherapy is potentially another effective treatment. Given the secular nature of society, this could well hold the key to an indirect method of effecting a spiritual re-awakening. It would be judicious if more meditators became involved in psychotherapy.

One should consider further: within meditation there is a repeated process of focusing and expansion of consciousness. How much does consciousness have to expand and in what direction? The potential is infinite, which makes it all the more important that obstacles within the mind are really penetrated systematically. Many of the psychic sideshows may be irrelevant and might easily become hindrances as has been recognised:

"The soul's beauty and capabilities are so immeasurably great that I can't think of anything that I can compare with it ... This being so, there is no point tiring ourselves out trying to take in the castle's beauty."

[Teresa of Avila, 'The Interior Castle', Chapter: 'The First Mansion']

So we should examine methods which, however odd at first sight, have enabled practitioners to demonstrably overcome mental obstacles and become spiritually transformed. These practitioners are sources of inspiration; once again I stress that it is most important that once you are committed to a method, you have a teacher or counsellor who has proceeded along the path you are following. Such transmission is essential, otherwise progress may be rather haphazard.

A Vector Model for a Spiritual Path

I offer below a crude theoretical map of the whole mind. Western psychology doesn't even seem to possess such a map - there are maps, perhaps of great detail and sophistication, but owing to limitations inherent in the (isolated rational) methods, such maps address only a few mental realms. Yet, unless there is an appreciation of the non-physical levels of mind, one cannot fathom, for instance, the teachings of Christ expressed in the gospels.

Once the map is drawn, one is then faced with the consideration of appropriate paths - there is a need for a sense of direction. These two elements are encapsulated in the notion of a vector.

Definition A vector is a quantity which possesses both magnitude (or quantity or scalar component) and direction.

An example of a vector is velocity: e.g., a ferry making a crossing from Uig to Tarbert (Hebridean towns off the coast of Scotland) may be said to have a velocity of 10 knots due West. Its magnitude is its speed of 10 knots and its direction is West.

I shall now construct some vectors for the spiritual path, starting with a description of the scalar component.

The suggestion of some Utility Values

It is only when one has completed a difficult journey that one really appreciates which were the crucial stages. This is especially true of the spiritual journey; until it is over, there can be at best a strong intuition about the major milestones and crossroads, but no certainty. However, before setting out, it is helpful to have some fair estimates of the types of terrain that lie ahead. Using this as an analogy for the scalar component of our spiritual journey, we may define the notion of a 'utility value'.

Definition: A utility value is the perceived worth of a given item, perhaps a material object, a psychological ability or an emotional state. This value may be expressed as a quantity.

Below I introduce some of my own utility values as guidelines concerning the various levels of mind and bring in also the necessary sense of direction, and their implications for any 'spiritual strategy.' These values are expressed in terms of 'generators' and the direction in terms of 'operators'.

The Notions of Generators and Operators

A painting may often be composed of hundreds, perhaps thousands of different colours, but it would be ludicrous for an artist to carry around dozens of palettes! All the artist needs is a small selection of primary colours plus creativity and imagination. These most basic colours, out of which countless colours may be invented, I term generators. To recreate even the subtlest shades, an artist simply plucks out the tiny palette and combines the primary colours in varying degrees.

A generator may be regarded as any basic psycho-physical building block. For instance, one may see on separate occasions first a small garden with flowers, sheltered by a couple of trees, and then a simple grassy mound. Later there may arise a vividly 'imagined' scene of a valley in bloom, surrounded by forests: here the two initial scenes acted as generators.

As another example, by listening carefully to a person's voice, for only a few seconds, one may establish the tone patterns which define that voice - generators - through which one may 'speak' thoughts in that voice in the 'mind's ear'.

Perhaps a more familiar example is that of DNA. DNA contains genetic code, using what may be modelled as certain permutations of just 4 letters (i.e. just 4 generators). According to theory, from this code there may be determined the inherited characteristics of all life on Earth 1.

The panorama depicted above may be a day-dream or a genuine alert creation; the former is an escapist ploy of the reactive mind when one's attention wanders, the latter a mindful spiritual expresssion. The reactive mind and the Spirit are what I term operators. They are the guiding forces in conduct and where lies in essence the famed duel between 'good and evil' - see also the discussion of memory in the next chapter.

This then is the crucial basis of the sense of direction.

Generators in Layers of Mind

One can view generators across the spectrum of layers of mind. Suppose that we number the layers 1 to N, say, where 1 = physical, N = deepest psychic. Then one may find that a generator in a deep level of mind has as an echo several generators in a more shallow level. As evidence to support this, consider the fact that a psychological illness often gives rise to several physiological illnesses, each of which in turn can manifest further pathologies. On the other hand, simple sublime compassion may blossom in the ability to generate a warm personality and powers to heal.

Alternatively, a deep-rooted generator may give rise to a succession of apparently small and insignificant abilities/ deficiencies, just one per level.

The Engram as Generator, Reactive Mind as Operator

A specific example of a (destructive) generator is the engram, a memory trace - with physical and non-physical components - of a traumatic incident with associated emotions; it has the property of being open to subsequent restimulation by the reactive mind, interrupting otherwise smooth consciousness, in the form of psychological problems. A combination of a few engrams may give rise to an encyclopaedia of phobias.

Engrams may be considered analogous to computer viruses - once they are 'sown' they act like little programs which are triggered in certain environments, causing advanced systems to suddenly suffer unsuspected abortive routines, causing tremendous inconvenience. It is often the case, however, that the hardware itself continues to function without fault - it just obeys somebody else's instructions! Through the anthropomorphic tendency to personify, one may regard these engrams and viruses as having a malevolent will of their own. However, despite their virulence and toxicity, there is no intelligence in them.

Engrams may occur, I conjecture, across at least all layers of conditioned mind. A healing process could involve the complete eradication of the debilitating source of the engrams, via the conscious recall of the original 'incidents' (which might be beyond linear time).

A systematic eradication is highly problematic and certainly beyond isolated rational analysis: for instance, suppose that for an individual all engrams across the physical level are eradicated (as far as can be seen to arise there at source). It may subsequently be the case that such an individual is somewhat mal-adjusted overall, spiritually quite lost and requiring further help. What we have here is only 'local optimisation' or 'local maximisation'.

Any system of local maximisation should be approached with great caution. Any system which puts forward in isolation e.g. the complete healing of the physical body ignores the essence of spirituality. An example of a 'locally logical' means for developing 'human potential', one that is, as it were, 1-dimensional in 3D reality, is genetic engineering - cracking the code in DNA. Anybody with some spiritual sensitivity can see that this area is highly dangerous - there are other more enlightened ways to human improvement.

However, any narrowly defined healing or purification process may point in the appropriate spiritual direction for some, though for others - e.g. those destined not to be reborn in a physical form - it may be a waste of time. If physical perfection were so important, then the saints would have all been athletes par excellence!

Application to Utility Values

To reflect the panoramic nature of mind, I feel that a suitable set of utility values should take into account the following.

  1. A broad a perspective as possible across all psycho-physical levels.
  2. Suitable decreased weighting from the subtlest psychic levels to the the crudest (=physical) level; those levels which persist through physical death may naturally carry more weight than those that don't.
  3. Given (1) and (2), the establishment of the goals within each level and sub-utility levels within each of these.
Using these as guidelines, one may model a transcendental path as an iterative counting process. Here, we count in binary.

Suppose we give a measure of ability in psychic level x a value between 0 and 2x, the higher the more able. Then one's total ability is the sum of all the abilities in the respective levels with the property that a full ability in level x alone exceeds in value full ability in all lower levels combined.

Suppose further that mind is given a status - ti. Then, we may illustrate a progression of mental states as follows.

e.g. Let x=4:

level: 4 3 2 1 0
'full ability' value: 16 8 4 2 1
status t1: 0 0 1 1 1
status t2: 0 1 0 0 0

For the status we write using the binary shorthand.

Then, the Total 'ability' Value at t1 is: 4+2+1=7;

whilst the Total 'ability' Value at t2 is: 8.

An individual's or society's evolution may be thus be mapped linearly in time by ascribing at each moment a value equal to the sum of its abilities. In due course, a trend may be observed, one which is approximately a kind of binary clock whereby one reaches the zenith of ability in a succession of levels (e.g., 00111 as above) and, carried on by momentum, crashes through into a higher level, but with great upheaval (hence, 01000). Christ's actions on the cross - his giving up of all material wealth and super-human abilities - effected such a momentous transition.

Utility values may help to give relative guidelines for a healing process which consists of stepping through the levels in overall uniform fashion. Such a process makes the critical assumption that it is valid to take a linear approach - which is not completely satisfactory since various levels may be non-linearly related. Considering the high level of abstraction, this may appear highly risky. However, a systematic linear approach can work overall if one is prepared to follow the trail as deep as is necessary at the appropriate moment. If one is excavating an unknown number of mines from a field to deactivate them, then it is usual to search thoroughly the whole of the site, only delving deeper whenever the mine detector sounds the alert.

Utility Vectors

The utility values supply magnitude only. Strictly speaking, we may only talk with certainty about magnitude, but obviously this is not good enough. So I suggest that direction may be included by the notion of a 'utility vector' which is computationally very similar in form to that of a utility value. The directional element is provided simply through the prefix of +1 or -1 to each level component which is then 'normalised' to give a single value that may be compared - a very simplistic notion of one's 'spiritual worth'.

In this model, one's spiritual worth "has the form":-

d1a1 + d2a2 + ... + dnan, where 0 <= al <= 21, dl = +1 or -1 The objective is to maximise this value.


Suppose we take status t1 (= 00111). Then the magnitudes are:-

    a0 = 1 * 20 = 1, 
    a1 = 1 * 21 = 2,
    a2 = 1 * 22 = 4,
    a3 = 0 * 23 = 0,
    a4 = 0 * 24 = 0

Now suppose that the respective direction elements are:-

    d0 = -1,
    d1 = -1, 
    d2 = +1, 
    d3 =  -1 or +1,  
    d4 =  -1 or +1

(d3 and d4 do not affect the total).

    a0d0 = -1 * 1 = -1, 
    a1d1 = -1 * 2 = -2,
    a2d2 = +1 * 4 = +4,
    a3d3          =  0,
    a4d4          =  0.
Then, the utility vector is:


The overall spiritual worth is the normalised utility vector, i.e. just the sum of the components: +4-2-1 = 1.

From this it is evident that the direction becomes doubly important at each successive level - the greater the ability, the greater the potential good or harm. One must know who handles the generators.


I have provided an abstract mathematical model of mind which is a very simplified view, but nevertheless delineates between distinct mental forms or realms. Through these distinctions I hope I redress just a little the massively imbalanced view of mind as a somehow equal dichotomy of physical and non-physical. I'm not differentiating between emotional states, but between distinct planes of existence.

I hope to indicate in the next chapter that such a multi-layered view is no mere flight of fancy since these kind of teachings have already existed for a long time.


  1. Ref: 'Cracking the Code' - BBC2 7/9/93. ^

Technical footnote

utility values are made from row vectors,
utility vectors are row vectors with simple +/- type vector components
The next experimental chapter is: Perspectives II | Contents Page

- Paul Trafford 1996,97 Paul's home page