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THE BOOK OF THE LAW
The physical description of the onset of this ecstasy refers to the actual facts at the period of receiving this knowledge.
The attempt to resolve All into One is a philosophical blunder. It explains nothing; neither how One came to be, nor how Two came to be. The only sound conception is that of "Zero not extended" with a phase of "Something" ("0 degree = X") which makes the answer to both questions self-evident.
The idea "One" is intelligible enough as the result of the resolutions of Two. But in itself it is meaningless because of the absence of any co-ordinates. A point can heave no qualities except as it is related to a second point. It is only 'high' if there be another which is 'low'. It cannot even be said to exist unless there be something which does not exist.
Note the word 'continuous' repeated. It suggests the "continuum" of modern mathematical philosophy.
On the other hand, the constitution of Nuit is 'atomic' (verse 26) or discontinuous. She is in fact the reconciliation of these contradictory ideas. It is important for us to grasp the philosophical situation formally; and this demands a some-what close analysis. The definitions of Cantorian and Dedekindian continuity should be sought in Bertrand Russell, Op. Cit.; it is sufficient here to explain that by the continuity of Nuit I conceive conditions similar to those of the sphere of water described in the quotation in the note to verse 25. Any point in this sphere would be indistinguishable from any other point in a certain sense; or at least the distinction might be considered as arbitrary and illusory. Yet there is no reason why we should not choose to fix our attention on any particular point or system of points for the purpose of amusing ourselves -- analogously to the explanation above put forward (notes on vv. 3 & 4) of incarnation. The constitution of our illusion will evidently be atomic. The facts that {...}, and that the subtraction of (a) the inductive numbers, (b) the inductive numbers greater than n, (c) the odd numbers, from {...} give respectively zero, n and {...} as the result, do not interfere with the finite character of the relation between n and n 1. The transfinite properties of {...} do not destroy the atomic character of the series of which it is the sum.
Let us investigate the nature of existing ideas a little more closely. First of all, Nuit, being the totality of possibilities of Form, is not only one series, but the sum of all series. We are justified in conceiving any collection of ideas soever as a homologous series, for we have the right to choose the function which will serve to arrange them as our design requires. To protest that such a choice is arbitrary, fantastic or irrational is to assert the authority of some self-appointed "normal mind" as absolute in Nature. The failure of philosophers to transcend their own mental limitations has reduced all their systems to circular arguments, and all their ontologies to Solipsism, however elaborately they have endeavoured to to cloak the fact with sophistries. You cannot tie a true knot in a cord with a closed circuit. All knowledge is relative to the mind which contains it.
Consider "incommensurable" numbers, such as 1 and 2. This coy surd is insensible to the fascinations of the deftest Dedekindian Cult. It may be approached within limits as narrow as we choose to appoint; yet there remains a "great gulf fixed" which is utterly impassable. The surd is simply not in the series; you might as well try to find Consciousness by making microtome sections of the brain. Yet the relation between 1 and 2 is perfectly clear and simple; there is no incommensurability about it at all. It is (for one thing) the ratio of the hypoteneuse of a right-angled isoceles triangle to one of the other sides, in Euclidian geometry. The difficulty of commensuration can exist only in minds obsessed by the atavistic necessity of counting cowries or wives on the fingers.
Let me then maintain that such collections as "The thoughts of a man's lifetime" constitute a series in the same sense as the inductive numbers. This collection conforms perfectly with Peano's 'ideas' and 'proposition'. Every thought is a thing in itself; it is determined by its predecessors and determines its successors; it is concatenated with them by 'psychological time'. Briefly, it fulfils every condition required by the definition. (The 'recurrenee' of a thought is no objection, for the identity is superficial, like that of a digit in a long decimal. "My aunt", whom I now think of, is not the aunt I thought of last year, any more than the 4 in the second place of .0494 is the same as that in the fourth place.)
Any thought in this series possesses a chain of sub-thoughts which connect it with its neighbours; these may be discovered by the proper psychological methods. "The Words of the insane are mountain-tops"; two successive thoughts may be compared to two snow summits rising above cloud-banks; they are not isolated, but joined by certain geologically necessary formations. But each pair of such sub-thoughts may be similarly investigated, and so on ad infinitum. Each thought is inevitably itself, although it is related to all other possible thoughts. There are not two thoughts of which we can say that one either merges into, or necessarily begets, the other. Any series of thoughts is therefore a true inductive series, exactly as the "natural numbers" are, with the added properties that it is real and omniform. It is atomic, its elements being intrinsically individual; and yet a continuum, since its intervals are susceptible of subdivision indefinitely prolonged without producing any diminution of these properties of the original series. The difference between successive thoughts and successive numbers is that by inserting r terms between p and q -- p:p : p 2 : --- p (2 -1) : q -- we apparently approximate the members, so that p-q (p 2)-(p ); while the sub-thoughts which intervene between my impression on waking "A fine frosty morning" and my reaction "I'll go skating" come to me from very various departments of my mind, and no two of them are in any way more closely connected than their culmination in consciousness is to its forerunner. But this difference is in reality an illusion born of the obsession already diagnosed; 2 is nearer to 1 and to 3 than 3 is to 1 only in respect of one particular function. Full comprehension of the true nature of number, as conceived by this Book, should enable the mind to transcend its "normal" trammels.
It will no doubt be objected that these speculations, even if correct, are sterile; or, even worse, discouraging to that study of the relations between phenomena which has been the basis of all advance in knowledge.
I might deny the reality of the progress, since it has only exposed the self-contradictions, and emphasized the mysteries, which beset us. But I prefer to take my stand on the ground that we have been totally wrong, hitherto, in our fundamental attitude to the Universe. The only possible issue from the vicious circle wherein we are penned is to refuse resolutely to allow ourselves to accept (1) the evidence of our senses, (2) the pleadings of our minds, (3) the reactions between phenomena as tokens of Truth. All objects are equally capable of conveying any given impression to us; it is merely a question of arranging the conditions of the experiments. We can add or subtract any conceivable quality at will. Thus, "there is no difference"; and each existence is inscrutably itself. We are only the more deceived as it multiplies its Protean projections.
Our proper course is to destroy the instruments of perception which we at present possess, recognizing that they are no more than personal prejudices which limit and delude us in every way. Our senses assure us that the earth is flat, and that the Sun moves across it, until we amend their assertions by the aid of instruments, and of reason. Yet the astronomer with his telescope is no less arbitrary than the cave-man with his eye. We are like the Snark in the Barrister's dream, witnesses, lawyers, and judge in one. We have no standard independent or ourselves; and we know only too well that our witnesses, the senses, are neither competent, clear, trustworthy, intelligent, or even capable of giving evidence on the actual issues.
The mid is in even worse plight. Obviously, its judgments must be based on its own laws, and we have no shadow of reason for supposing that these possess any authority beyond their own jurisdiction. We know that the Structure of the brain has been determined by the animal struggle to survive: it is adapted to the conditions of environment. It is the serf of brute passions, the ape of atavism, the dupe of sense, and the automaton of accident. We have no right to assert that its internal reactions correspond to the external world in any way whatever. Officially recognized thinkers are only just beginning to realize what mystics have known since the Morning Star glimmered through the haze on the horizon of History, that the Laws of Thought are only expressions of the bondage of the thinker. Apart from the dependence of mind upon the unreliable, symbolically communicated, and fragmentary affidavits of sense, apart from the imperfections inseparable from its origin, our judgments are necessarily no more than representations of the consistency of one part of our internal structure with another. We cannot lift ourselves by pulling at our toes. We now know that our most fixed axioms are as arbitrary as a madman's delusions. There is nothing to prevent a man from asserting that "Things which are both equal to the same thing are both greater than each other" and constructing a geometry conformable thereto: neither by reasoning nor by experience could it be proved that his system was not the "truth" of Nature. More, the word "truth" itself has proved on analysis to contain no intelligible significance, but to be an empirical symbol of what can only be described as symptoms of cerebral inadequacy.
Still worse, even so far as the conclusions of reason express the relations of an animal with itself, they disclose not the consistency which is the test of the fulfilment of this limited function, but an inherent self-contradiction which shatters the validity of the entire process. For the "Law of Contradiction" is the Court of final Appeal which has been the authority for every step. I quote once more from the Hon. Bertrand Russell, Op. Cit.:
"The comprehensive class we are considering, which is to embrace everything, must embrace itself as one of its members. In other words, if there is such a things as "everything", then "everything" is something, and is a member of the class "everything". But normally a class is not a member of itself. Mankind, for example, is not a man. Form now the assemblage of all classes which are not members of themselves. This is a class: is it a member of itself or not? If it is, it is one of those classes that are not members of themselves, i.e. it is a member of itself. Thus of the two hypotheses -- that it is, and that it is not, a member of itself -- each implies its contradictory. This is a contradiction, similar contradictions ad lib." {WEH NOTE: I'm sorry. I just can't keep shut. This is just the bloody fallacy of FOUR TERMS!}
This author, perhaps the mightiest mind of its type now living, proceeds gallantly to go "over the top". But he is always, sooner or later, drowned in the "blood" of a new contradiction, or the "mud" of mystery. He finds himself constantly compelled to assume some axiom which has been proved to be incapable of being proved, or crushed by the certainty that even in the event of his proving all his propositions, the sum of their statement amounts to this, that, so far as he is anybody or anything, he is himself.
Professor Eddington, in the masterly exposition of modern thought already quoted, presents, clearly enough, the case against supposing that any phenomenon soever is a "fact" in any absolute sense.
Each account of it must be incomplete, symbolic, and variable with the position and faculties of the observer.
"By his theory of relativity, Albert Einstein has provoked a revolution of thought in physical science."
"The achievement consists essentially in this: -- Einstein has succeeded in separating far more completely than hitherto the share of the observer and the share of external nature in the things we see happen. The perception of an object by an observer depends on his own situation and circumstances; for example, distance will make it appear smaller and dimmer. We make allowance for this almost unconsciously in interpreting what we see. But it now appears that the allowance made for the motion of the observer has hitherto been too crude, -- a fact overlooked because in practice all observers share nearly the same motion, that of the earth. Physical space and time are found to be closely bound up with this motion of the observer; and only an amorphous combination of the two is left inherent in the external world. When space and time are relegated to their proper source -- the observer -- the world of nature which remains appears strangely unfamiliar; but it is in reality simplified, and the underlying unity of the principal phenomena from this new outlook have, with one doubtful exception, been confirmed when tested by experiment."
I must confess that I was amazed with every amazement when so the the eminent astronomer failed to follow up this brilliant outburst by turning the devastation of his artillery upon the ramparts of the citadel whose outlying defenses he had shattered with such stupendous thunderbolts. Now came it that the very act of detecting so subtly, and removing so skillfully, the mote in his neighbour's eye, did not suggest to him that he might be incommoded by the beam of his own? Aware of the errors introduced into his calculations by the comparatively steady, regular, and imperceptible motion of his earth-borne body, how not to be stricken aghast to contemplate the possible consequences of taking, as a fixed and absolute point for the base of his triangulations, and unknown and uncontrollable engine in violent, erratic and incalculable action, neither to be mastered nor measured, his mind? Who dare presume to set limits to the eccentricities of a brain which is the logical conclusion for a love-harried, witch-burning, god-fearing, fox-hunting, cannibal ape, spice with tubercle, syphilis, insanity and the rest of the poisons for one premise and an unintelligible and accidental environment for the other? Is not every thought determined, and its validity indeterminable, especially by its owner? Who then shall decide what "trustworthy reasoning" may mean?
At the very least, we must eliminate as far as possible very obvious source of error, such as personality (in particular) involves. But further, we must regulate the motion of the mind, control it, bring it to a standstill. It may be -- I know that it is -- that as soon as thought is prevented from bewildering us with its torrential turmoil, we may become aware that we posses a subtler and steadier organ of apprehension. This is in fact one of the principal points of initiation.
The attempt to resolve All into One is a philosophical blunder. It explains nothing; neither how One came to be, nor how Two came to be. The only sound conception is that of "Zero not extended" with a phase of "Something" ("0 degree = X") which makes the answer to both questions self-evident.
The idea "One" is intelligible enough as the result of the resolutions of Two. But in itself it is meaningless because of the absence of any co-ordinates. A point can heave no qualities except as it is related to a second point. It is only 'high' if there be another which is 'low'. It cannot even be said to exist unless there be something which does not exist.
Note the word 'continuous' repeated. It suggests the "continuum" of modern mathematical philosophy.
On the other hand, the constitution of Nuit is 'atomic' (verse 26) or discontinuous. She is in fact the reconciliation of these contradictory ideas. It is important for us to grasp the philosophical situation formally; and this demands a some-what close analysis. The definitions of Cantorian and Dedekindian continuity should be sought in Bertrand Russell, Op. Cit.; it is sufficient here to explain that by the continuity of Nuit I conceive conditions similar to those of the sphere of water described in the quotation in the note to verse 25. Any point in this sphere would be indistinguishable from any other point in a certain sense; or at least the distinction might be considered as arbitrary and illusory. Yet there is no reason why we should not choose to fix our attention on any particular point or system of points for the purpose of amusing ourselves -- analogously to the explanation above put forward (notes on vv. 3 & 4) of incarnation. The constitution of our illusion will evidently be atomic. The facts that {...}, and that the subtraction of (a) the inductive numbers, (b) the inductive numbers greater than n, (c) the odd numbers, from {...} give respectively zero, n and {...} as the result, do not interfere with the finite character of the relation between n and n 1. The transfinite properties of {...} do not destroy the atomic character of the series of which it is the sum.
Let us investigate the nature of existing ideas a little more closely. First of all, Nuit, being the totality of possibilities of Form, is not only one series, but the sum of all series. We are justified in conceiving any collection of ideas soever as a homologous series, for we have the right to choose the function which will serve to arrange them as our design requires. To protest that such a choice is arbitrary, fantastic or irrational is to assert the authority of some self-appointed "normal mind" as absolute in Nature. The failure of philosophers to transcend their own mental limitations has reduced all their systems to circular arguments, and all their ontologies to Solipsism, however elaborately they have endeavoured to to cloak the fact with sophistries. You cannot tie a true knot in a cord with a closed circuit. All knowledge is relative to the mind which contains it.
Consider "incommensurable" numbers, such as 1 and 2. This coy surd is insensible to the fascinations of the deftest Dedekindian Cult. It may be approached within limits as narrow as we choose to appoint; yet there remains a "great gulf fixed" which is utterly impassable. The surd is simply not in the series; you might as well try to find Consciousness by making microtome sections of the brain. Yet the relation between 1 and 2 is perfectly clear and simple; there is no incommensurability about it at all. It is (for one thing) the ratio of the hypoteneuse of a right-angled isoceles triangle to one of the other sides, in Euclidian geometry. The difficulty of commensuration can exist only in minds obsessed by the atavistic necessity of counting cowries or wives on the fingers.
Let me then maintain that such collections as "The thoughts of a man's lifetime" constitute a series in the same sense as the inductive numbers. This collection conforms perfectly with Peano's 'ideas' and 'proposition'. Every thought is a thing in itself; it is determined by its predecessors and determines its successors; it is concatenated with them by 'psychological time'. Briefly, it fulfils every condition required by the definition. (The 'recurrenee' of a thought is no objection, for the identity is superficial, like that of a digit in a long decimal. "My aunt", whom I now think of, is not the aunt I thought of last year, any more than the 4 in the second place of .0494 is the same as that in the fourth place.)
Any thought in this series possesses a chain of sub-thoughts which connect it with its neighbours; these may be discovered by the proper psychological methods. "The Words of the insane are mountain-tops"; two successive thoughts may be compared to two snow summits rising above cloud-banks; they are not isolated, but joined by certain geologically necessary formations. But each pair of such sub-thoughts may be similarly investigated, and so on ad infinitum. Each thought is inevitably itself, although it is related to all other possible thoughts. There are not two thoughts of which we can say that one either merges into, or necessarily begets, the other. Any series of thoughts is therefore a true inductive series, exactly as the "natural numbers" are, with the added properties that it is real and omniform. It is atomic, its elements being intrinsically individual; and yet a continuum, since its intervals are susceptible of subdivision indefinitely prolonged without producing any diminution of these properties of the original series. The difference between successive thoughts and successive numbers is that by inserting r terms between p and q -- p:p : p 2 : --- p (2 -1) : q -- we apparently approximate the members, so that p-q (p 2)-(p ); while the sub-thoughts which intervene between my impression on waking "A fine frosty morning" and my reaction "I'll go skating" come to me from very various departments of my mind, and no two of them are in any way more closely connected than their culmination in consciousness is to its forerunner. But this difference is in reality an illusion born of the obsession already diagnosed; 2 is nearer to 1 and to 3 than 3 is to 1 only in respect of one particular function. Full comprehension of the true nature of number, as conceived by this Book, should enable the mind to transcend its "normal" trammels.
It will no doubt be objected that these speculations, even if correct, are sterile; or, even worse, discouraging to that study of the relations between phenomena which has been the basis of all advance in knowledge.
I might deny the reality of the progress, since it has only exposed the self-contradictions, and emphasized the mysteries, which beset us. But I prefer to take my stand on the ground that we have been totally wrong, hitherto, in our fundamental attitude to the Universe. The only possible issue from the vicious circle wherein we are penned is to refuse resolutely to allow ourselves to accept (1) the evidence of our senses, (2) the pleadings of our minds, (3) the reactions between phenomena as tokens of Truth. All objects are equally capable of conveying any given impression to us; it is merely a question of arranging the conditions of the experiments. We can add or subtract any conceivable quality at will. Thus, "there is no difference"; and each existence is inscrutably itself. We are only the more deceived as it multiplies its Protean projections.
Our proper course is to destroy the instruments of perception which we at present possess, recognizing that they are no more than personal prejudices which limit and delude us in every way. Our senses assure us that the earth is flat, and that the Sun moves across it, until we amend their assertions by the aid of instruments, and of reason. Yet the astronomer with his telescope is no less arbitrary than the cave-man with his eye. We are like the Snark in the Barrister's dream, witnesses, lawyers, and judge in one. We have no standard independent or ourselves; and we know only too well that our witnesses, the senses, are neither competent, clear, trustworthy, intelligent, or even capable of giving evidence on the actual issues.
The mid is in even worse plight. Obviously, its judgments must be based on its own laws, and we have no shadow of reason for supposing that these possess any authority beyond their own jurisdiction. We know that the Structure of the brain has been determined by the animal struggle to survive: it is adapted to the conditions of environment. It is the serf of brute passions, the ape of atavism, the dupe of sense, and the automaton of accident. We have no right to assert that its internal reactions correspond to the external world in any way whatever. Officially recognized thinkers are only just beginning to realize what mystics have known since the Morning Star glimmered through the haze on the horizon of History, that the Laws of Thought are only expressions of the bondage of the thinker. Apart from the dependence of mind upon the unreliable, symbolically communicated, and fragmentary affidavits of sense, apart from the imperfections inseparable from its origin, our judgments are necessarily no more than representations of the consistency of one part of our internal structure with another. We cannot lift ourselves by pulling at our toes. We now know that our most fixed axioms are as arbitrary as a madman's delusions. There is nothing to prevent a man from asserting that "Things which are both equal to the same thing are both greater than each other" and constructing a geometry conformable thereto: neither by reasoning nor by experience could it be proved that his system was not the "truth" of Nature. More, the word "truth" itself has proved on analysis to contain no intelligible significance, but to be an empirical symbol of what can only be described as symptoms of cerebral inadequacy.
Still worse, even so far as the conclusions of reason express the relations of an animal with itself, they disclose not the consistency which is the test of the fulfilment of this limited function, but an inherent self-contradiction which shatters the validity of the entire process. For the "Law of Contradiction" is the Court of final Appeal which has been the authority for every step. I quote once more from the Hon. Bertrand Russell, Op. Cit.:
"The comprehensive class we are considering, which is to embrace everything, must embrace itself as one of its members. In other words, if there is such a things as "everything", then "everything" is something, and is a member of the class "everything". But normally a class is not a member of itself. Mankind, for example, is not a man. Form now the assemblage of all classes which are not members of themselves. This is a class: is it a member of itself or not? If it is, it is one of those classes that are not members of themselves, i.e. it is a member of itself. Thus of the two hypotheses -- that it is, and that it is not, a member of itself -- each implies its contradictory. This is a contradiction, similar contradictions ad lib." {WEH NOTE: I'm sorry. I just can't keep shut. This is just the bloody fallacy of FOUR TERMS!}
This author, perhaps the mightiest mind of its type now living, proceeds gallantly to go "over the top". But he is always, sooner or later, drowned in the "blood" of a new contradiction, or the "mud" of mystery. He finds himself constantly compelled to assume some axiom which has been proved to be incapable of being proved, or crushed by the certainty that even in the event of his proving all his propositions, the sum of their statement amounts to this, that, so far as he is anybody or anything, he is himself.
Professor Eddington, in the masterly exposition of modern thought already quoted, presents, clearly enough, the case against supposing that any phenomenon soever is a "fact" in any absolute sense.
Each account of it must be incomplete, symbolic, and variable with the position and faculties of the observer.
"By his theory of relativity, Albert Einstein has provoked a revolution of thought in physical science."
"The achievement consists essentially in this: -- Einstein has succeeded in separating far more completely than hitherto the share of the observer and the share of external nature in the things we see happen. The perception of an object by an observer depends on his own situation and circumstances; for example, distance will make it appear smaller and dimmer. We make allowance for this almost unconsciously in interpreting what we see. But it now appears that the allowance made for the motion of the observer has hitherto been too crude, -- a fact overlooked because in practice all observers share nearly the same motion, that of the earth. Physical space and time are found to be closely bound up with this motion of the observer; and only an amorphous combination of the two is left inherent in the external world. When space and time are relegated to their proper source -- the observer -- the world of nature which remains appears strangely unfamiliar; but it is in reality simplified, and the underlying unity of the principal phenomena from this new outlook have, with one doubtful exception, been confirmed when tested by experiment."
I must confess that I was amazed with every amazement when so the the eminent astronomer failed to follow up this brilliant outburst by turning the devastation of his artillery upon the ramparts of the citadel whose outlying defenses he had shattered with such stupendous thunderbolts. Now came it that the very act of detecting so subtly, and removing so skillfully, the mote in his neighbour's eye, did not suggest to him that he might be incommoded by the beam of his own? Aware of the errors introduced into his calculations by the comparatively steady, regular, and imperceptible motion of his earth-borne body, how not to be stricken aghast to contemplate the possible consequences of taking, as a fixed and absolute point for the base of his triangulations, and unknown and uncontrollable engine in violent, erratic and incalculable action, neither to be mastered nor measured, his mind? Who dare presume to set limits to the eccentricities of a brain which is the logical conclusion for a love-harried, witch-burning, god-fearing, fox-hunting, cannibal ape, spice with tubercle, syphilis, insanity and the rest of the poisons for one premise and an unintelligible and accidental environment for the other? Is not every thought determined, and its validity indeterminable, especially by its owner? Who then shall decide what "trustworthy reasoning" may mean?
At the very least, we must eliminate as far as possible very obvious source of error, such as personality (in particular) involves. But further, we must regulate the motion of the mind, control it, bring it to a standstill. It may be -- I know that it is -- that as soon as thought is prevented from bewildering us with its torrential turmoil, we may become aware that we posses a subtler and steadier organ of apprehension. This is in fact one of the principal points of initiation.
The dyad (or universe) is created with little pain in order to make the bliss of dissolution possible. Thus the pain of life may be atoned for by the bliss of death.
This delight is, however, only for the chosen servants of Nu. Outsiders may be looked on much as the Cartesians looked on animals. Yet, of course, this is only on the plane of Illusion. One must not discriminate between the space marks. (P.S. The Christian is one who has acquiesced in his own dishonour; a renegade from manhood).