The Cube-root of Zero

(pub. The Middle Way, May 1965. The Tenth Man (HKU Press, 1966) Part II, Ch. 31.)


Many articles and some books have been written about further directions of measurement than the three which are available to our sensory apparatus, and in several European languages. As far as I am aware all are concerned exclusively with what may be called 'the search for the Nth dimension', while higher mathematics, by the use of symbols, can use such suppositional directions of measurement for its own theoretical purposes.

All are searching for something, and these earnest searchers have never found anything. Strange to say, this seems odd to them. Yet the explanation is evident for all to see.

What are directions of measurement? They are measurements from here to there. They can be represented objectively; for instance a line can be drawn from A to B, and that represents length; then a line can be drawn at right-angles to that, from A to B1, and that represents width, which, together with the former, constitutes a plane surface; then a further line can be drawn, or erected as a model, also at right-angles, from A to B2, and that represents height, all three directions constituting what is called volume, which is also what we know as 'space'. But all are measurements from A, and A is the centre from which all measurements are made. And what is A? A is the measurer, A is what measures, A is the centre of the universe, A is what we suppose ourselves to be, whoever we are and wherever we are. And since it is A who is now measuring, A is trying to measure itself. That is why there is nothing to be found.

There is no term or description which is adequate for a further direction of measurement, and that for the same reason, i.e. because there is nothing further that is objective to be measured, objectivity being defined by three dimensions only. And no descriptive indication of what is implied has ever been found that is better than that of Jesus - which was simply the word 'within'.

Within what? That is the question. Is there any thing within which a further measurement could be made? What is being searched for is neither behind the beyond nor within the inside, for such are concepts, but just plain here and now. Whether that has been understood or not, it is doubtless the underlying meaning of the tentative definition which declares that 'time is the fourth dimension of space', which is said to have found general acceptance among advanced physicists. Metaphysically we know, as has been explained heretofore, that what we conceive as 'time' is an aspect of what we ourselves appear to be, since without extension in duration phenomena could not be perceived, but multiplying and numbering purely mathematical directions of unimaginable measurement is of technical application only, and has no factual application whatever: it is sufficient to refer to directions of measurement, beyond the three which are sensorially perceptible to us, simply as the Nth dimension.

Since the three directions which are accessible to us describe the universe which is apparent, they are our objective measurements, and no further direction can be such, since our sensory equipment can know no further direction that can be objectified. It follows necessarily that an Nth dimension must be non-objective to us, which is a definition of what noumenally we are. In short it indicates noumenality. The 'kingdom of Heaven' may be a poetic definition, in itself a conceptual objectivisation, but no definition can be otherwise; what it ultimately indicates is our ultimate noumenality.

The searchers have been searching for what was searching, and they have found nothing but mathematical formulae because nothing but mathematical formulae is there to be found, that is to say the most abstract degree of conceptualisation. They were, and no doubt still are, searching for a universe outside the universe which is what they themselves are. In Huang Po's phrase, they are using mind to find mind, and mind cannot find mind any more than an eye can see itself. Noumenon cannot apprehend noumenon otherwise than as phenomena - and here there is none to be apprehended. We are the Nth dimension, which, therefore, is in no direction of measurement from us, and that can not be described, description being objectivisation, because being non-objectivity it cannot objectify itself since it is no thing to be objectified. Every centre of timeless infinity, which in appearance is everywhere and always, can objectify that which is phenomenal, but never can it objectify its own noumenality which is all that it is.



Phenomena and space-time are inseparable: their appearance is interdependent.
Noumenon is non-spatiality and timelessness: the absence itself of all concepts which need extension.
Space-time then is seen as an open gate to metaphysical comprehension.

As long as the concept of space-time is present, only phenomenal comprehension is possible - for only phenomenal comprehension is extended in space and duration.
The absence of the concept of space-time leaves noumenality omnipresent (ubiquitous and eternal), for there is no longer a space or a duration in which anything objective whatsoever can extend.
This abolition, dis-appearance of space-time, then will leave us integrally what we are.

The Great Joke, therefore, is seen to be the apprehension that our suppositional 'bondage' is our dependence on the notion of space-time which alone is responsible for the illusion on which the notion of 'bondage' depends.

Note: Phenomenally, we can know no present, since it must be in the 'past' before our senses can complete the process of recording it, leaving only a suppositional past and future; noumenally there is no question of 'past' or 'future' but only a presence which knows neither 'time' nor 'space'.


Awakening is waking-up to what is Here


The further or 'Nth' direction of measurement, which indicates where we are, which is Here and Now, is inaccessible alike to sensorial perception and to conceptualisation - the five senses and the conceptualising sixth. We need not doubt the reason for this, which indeed is obvious: it is simply because, being Here and Now, it is itself the centre from which externalisation takes place, and subject cannot objectify itself as subject. Therefore it can only be known in the total absence of conceptualisation.

This is why absence of mentation, of which conation is an element, has been universally recognised as an essential condition of what has been picturesquely termed awakening to 'enlightenment', more accurately 'disidentification'. Conation, or volition, being a direct expression of the subjective, or egotic, aspect of mentation, precludes any possibility of such inseeing - since that is outseeing from a psychic subject which itself is an object and, as such, purely conceptual.

But since we are evidently 'lived' - or 'dreamed' if you prefer - from our common centre in the nearer or Nth dimension, it is from this direction of measurement, our noumenal centre, that all direct, spontaneous and inevitable action or 'God's will', originates, rather than from the phenomenal or pseudo-centre of an egotic subject of conceptualised objects, whose effects are only appearance.

All accounts of direct experience by those who have found their way back - if I may so express it - to their eternal centre, be it called Nirvana, Dharmakaya, Butatathata, Buddha-Mind, True Nature, Self, Tao, Kingdom of Heaven, or anything else, confirm that this noumenal source, or true centre of each and all sentient beings is this tri-dimensionally void I-ness, from which all that is phenomenal originates.

We can deify it if we wish, and term it 'divine' as opposed to 'human', 'Heaven' as opposed to 'Earth', but what it is calls for no devotional or affective approach, which must necessarily conceal it as effectively as an intellectual search. Never could it be 'found' - for what it is, where it is, and when it is, is precisely what, where, and when, the searcher is who is seeking.

Note: It may be desirable to recall that 'space' is here a concept which provides exteriorised objects with the extension necessary to render their appearance 'solid', i.e. perceptible tri-dimensionally as objects, and in spatial relation to other objects, just as 'time' is their equally necessary extension in duration. Time is, therefore, an extension of space in duration, and so a further direction of measurement. Space-time as a single concept then utilises four dimensions, three spatial and one temporal.

Space-time, therefore, is an aspect of what phenomenally we appear to be - since it necessarily accompanies our appearance. 'Dimensions', being spatial measurement, i.e. a conceptual analysis of a concept (space or space-time), a further direction, or the 'Nth dimension', although itself no more than a conceptual analysis of what we appear to be, is one that leads us directly and inevitably to the noumenal source of our appearance which is, therefore, what we are and all that we are.

Note: For those concerned with the doctrines of various forms of Buddhism, or as propounded by successive Buddhas, the Nth or inclusive measurement of volume is what is variously described as 'the Void', 'the Middle Way', and 'Dependent Origination'. The first is fairly obvious, but the second is senseless as translated, being neither a 'way' nor in the 'middle' of anything; if conceivable as a 'way' it would need to be described as 'the Inner' or 'the Transcending' Way. The third may be said to find its explanation in super-volume.

(© HKU Press, 1966)
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