Tertium Organum (P.D. Ouspensky) · 164 of 225 · tr. Nicholas Bessaraboff and Claude Bragdon
Chapter XXI (part 2)
Science cannot deny the fact that mathematics grows, expands, and escapes from the limits of the visible and measurable world.
Entire departments of mathematics take into consideration quantitative relations which did not and do not exist in the real world of p.
256 positivism, i.e., relations which have no correspondence to any realities in the visible, three-dimensional world.
But there cannot be any mathematical relations to which the relation of some realities would not correspond.
Therefore mathematics transcends the limits of our world, and penetrates into a world unknown.
This is the telescope , by the aid of which we begin to investigate the space of many dimensions with its worlds.
Mathematics goes ahead of our thought, ahead of our power of imagination and perception.
Even now it is engaged in calculating relations which we cannot imagine or comprehend.
It is impossible to deny all this, even from the strictly "positivistic," i.e., positive standpoint.
Thus science, having admitted the possibility of the expansion of mathematics beyond the limits of the sensuously perceived world—that is beyond the limits of a world accessible (though theoretically) to the organs of sense and their mechanical aids—must thereby recognize the expansion of the real world far beyond the limits of any "infinite sphere" or of our logic, i.e., must recognize the reality of "the world of many dimensions." The recognition of the reality of the world of many dimensions is the already accomplished transition to, and understanding of, the world of the wondrous.
And this transition to the wondrous is impossible without the recognition of the reality of new logical relations which are absurd and impossible from the standpoint of our logic.
What are the laws of our logic?
They are the laws of our receptivity of the three-dimensional world , or the laws of our three-dimensional receptivity of the world .
If we desire to escape from the three-dimensional world and go farther, we must first of all work out the fundamental logical principles which would permit us to observe the relations of things in a world of many dimensions—seeing in them a certain reasonableness, and not complete absurdity.
If we enter there armed only with the principles of the logic of the three-dimensional world, these principles will drag us back, will not give us a chance to rise from the earth.
First of all we must throw off the chains of our logic.
This is the first, the great, the chief liberation toward which humanity p.
257 must strive.
Man, throwing off the chains of "three-dimensional" logic, has already penetrated, in thought, into another world.
And not only is this transition possible, but it is accomplished constantly.
Although unhappily we are not entirely conscious of our rights in "another world," and often sacrifice these rights, regarding ourselves as limited to this earthly world, paths nevertheless exist.
Poetry, mysticism, the idealistic philosophy of all ages and peoples, preserve the traces of such transitions.
Following these traces, we ourselves can find the path.
Ancient and modern thinkers have given us many keys with which we may open mysterious doors; many magical formulæ, before which these doors open of themselves.
But we have not understood either the purpose of these keys or the meaning of the formulæ.
We have also lost the understanding of magical ceremonies and rites of initiation into mysteries which had a single purpose: to help this transformation in the soul of man.
Therefore the doors remained closed, and we even denied that there was anything whatever behind them; or, suspecting the existence of another world, we regarded it as similar to ours, and separate from ours, and tried to penetrate there unconscious of the fact that the chief obstacle in our path was our own division of the world into this world and that .
The world is one , only the ways of knowing it are different; and with imperfect methods of knowledge it is impossible to penetrate into that which is accessible to perfect methods only.
The transformation of base substance — outer matter or the inner soul — into a purified, perfected, or 'gold' state; the magnum opus as both laboratory practice and spiritual allegory.
The text mentions rites of initiation designed to help 'this transformation in the soul of man,' echoing alchemical spiritual transformation.
Eckhart's Abgeschiedenheit/Gelassenheit — radical letting-go of will, image, and grasping that opens the soul to God; distinct from inner_silence (quietness) and from material renunciation, and adjacent to Sufi tark and Buddhist non-grasping as a practice rather than a metaphysical claim.
The instruction to 'throw off the chains of our logic' parallels the practice of letting go of mental constructs to access higher states.
The doctrine of the universe as boundless and without center or circumference, populated by innumerable worlds — Bruno's rejection of the closed Aristotelian sphere; the divine and the cosmos as ontologically infinite.
The text explicitly discusses the expansion of the real world beyond any 'infinite sphere' into a space of many dimensions and worlds.
Gurdjieff and Ouspensky's claim that ordinary human beings live in a state of waking sleep, reacting mechanically without unified will or consciousness, and that the spiritual path begins with recognising this condition.
The passage reflects Ouspensky's core theme that humans are unconscious of their rights in another world and regard themselves as limited to the earthly realm.
Numbers, proportions, and mathematical relationships as the underlying structure of divine reality.
[auto] The passage explicitly identifies mathematics as the primary tool that transcends visible limits and reveals the structure of higher dimensional realities.
Using apparent contradiction, reversal, or riddle to destabilise ordinary understanding and induce insight.
The text states that understanding higher worlds requires recognizing logical relations that are 'absurd and impossible from the standpoint of our logic.'
Iamblichean ritual practice that engages the gods directly through consecrated material symbols and actions, on the premise that divine power descends into properly prepared matter — distinct from philosophical contemplation alone.
The passage acknowledges 'magical ceremonies and rites of initiation' as historical tools for spiritual transformation, though their meaning is lost.