“Now I make another line to cross it at right angles. That is one extension in a second dimension.”
“I see, and another line would make a third dimension.”
“Don’t go too fast. Your third line is no use. If I want to show the position of any point on the paper, I can do it by reference to these two lines only. Make a point, and I’ll show you.”
She obeyed.
“Now, I draw lines from your point to make right angles with my lines. I say your point is so far east of the central point, and so far north. You see? I determine the position by only two measurements.”
“But if I made my point right in the air here?”
“Exactly. We need a third line, but it must be at right angles to the other two; sticking straight up, as you might say. Then we can measure in three directions, and determine the point. It is so far east, so far south, and so high.”
“Yes.”
“Now I’ll go over that again in another way.
“Here is a point, not long nor broad nor thick: no dimension.
“Here is a line, long but neither broad nor thick: one dimension. Here is a surface, long and broad, but not thick: two dimensions.
“Here is a solid, long and broad and thick: three dimensions.”
“Now I quite understand. But you said: four dimensions.”
“I will say it presently. But just now I am going to hammer at two.
“Observe: I make a triangle. All the sides are equal. Now I draw a line through it from one angle to the middle of the other side. I have two triangles. They are exactly alike, as you see; same size, same shape. But – they point in opposite directions. Now we will cut them out with scissors.”
He did so.
“Slide them about, so that one lies exactly to cover the other!”
She tried and failed: then, with a laugh, turned one over, when it easily fitted.
“Ah, you cheated. I said, ‘slide them’.”
“I’m sorry.”
“On the contrary, you have acted divinely, in the best sense! You took the thing that wouldn’t fit out of its world of two into the world of three, put it back, and they all lived happy ever after!
“The next thing is this. Everything that exists – everything material – has these three dimensions. These points and lines and surfaces have all a minute extension in some other dimension, or they would be merely things in our imagination. The surface of water, for instance, is merely the boundary between it and the air.
“Now I am going to tell you why some people have thought that another dimension might exist. Those triangles, so like, yet so unlike, have analogies in the world of what we call real things. For example there are two kinds of sugar, exactly alike in every way but one. You know how a prism bends a ray of light? Well if you take a hollow prism, and fill it with a solution of one of these kinds of sugar, the ray bends to the right; use the other kind, and it bends to the left. Chemistry is full of these examples.
“Then we have our hands and feet; however we move about, we can never make them fill exactly the same place. A right hand is always a right hand, however you move it. It only becomes a left hand in a looking-glass – so your mirror should in future afford you a superior sort of reflection! It should remind you that there is a looking-glass world, if you could only get through!”
“Yes, but we can’t get through!”
“Don’t let us lose our way! Enough to say that there might be such a world. But we must try to find a reason for thinking that there is one. Now the best reason of all is a very deep one; but try to understand it.”
Lisa nodded.
“We know that the planets move at certain rates in certain paths, and we know that the laws which govern them are the same as those which made Newton’s apple fall. But Newton couldn’t explain the law, and he said that he found himself quite unable to imagine a force acting at a distance, as gravitation (so called) appears to do. Science was hard put to it, and had finally to invent a substance called the ether, of which there was no evidence, only it must be there! But this ether had so many contradictory and impossible qualities, that people began to cast about for some other explanation. And it was found that by supposing an extension of the universe (thin but uniform) in a fourth dimension, that the law would hold good.
“I know it’s hard to grasp the idea; let me put it to you this way. Take this cube. Here is a point, a corner, where the three bounding lines join. The point is nothing, yet it is part of the lines. To imagine it at all as a reality, we must say that it has a minute extension in these lines.
“Now take a line. It has a similar minute uniform extension in the two surfaces which it bounds. Take the surface; it is similarly part of the one cube.
“Go one step further; imagine that the cube is related to some unknown thing as the surface is to the cube. You can’t? True; you can’t make a definite image of it; but you can form an idea – and if you train yourself to think of this very hard, presently you will get a little closer to it. I’m not going to bother you much longer with this dry theoretical part; I’ll only just tell you that a fourth dimension, besides explaining the difficulties of gravitation, and some others, gives us an idea of how it is that there is only a definite fixed number of kinds of things, from which all others are combined.
“And now we can get down to business. Brother Cyril, who obliged with the cube, will be so good as to produce a wooden cone and a basin of water.”
Brother Cyril complied.
“I want you to realise,” went on the old man, “that all the talk about the Progress of Science is cheap journalism. Most of the boasted progress is mere commercial adaptation of science, as who should say that he is Experimenting with Electricity when he rides in an electric train. One hears of Edison and Marconi as ‘men of science’; neither of them ever discovered a single fact; they merely exploited facts already known. The real men of Science are in absolute agreement that the advance in our knowledge, great as it has been, leaves us as ignorant of ultimate truth and reality as we were ten thousand years ago. The universe guards its secret: Isis can still boast that no man hath lifted her veil!
“But, suppose our trouble were due to the fact that we only received our impressions in disconnected pieces. A very simple thing might seem the maddest jumble. Ready, Cyril?”
“Quite ready.”
“I. A. A. I. U. I. A.”
“R. F. G. L. S. L.”
“What were we saying?”
Lisa laughed rather excitedly. Her vivid mind told her that these instructions were going to take sudden shape.
“Only your very pretty name, my dear! Now, Cyril, the cone.” He took it in his hand, and poised it over a bowl of water.
“We are now going to suppose that this very simple object is going to try its best to explain its nature to the surface of the water, which we will imagine as endowed with powers of observation and reasoning equal to our own. All that the cone can do is to show itself to the water, and it can only impress the water by touching it.
“So it dips its point, thus. The water perceives a point. The cone goes on dipping. The water sees a circle round where the point was. The cone goes on. The circle gets bigger and bigger. Suddenly, as the cone goes completely through, snap!
“Now, what does the water know?
“Nothing about any cone. If it got any idea that the various commotions were caused by a single object, which it would only do if it compared them carefully, noted a regularity of rate of increase in the size of the circle, and so on – in other words, used the scientific method – it would not evolve a theory of a cone, for we must remember that any solid body is to it a thing as wildly inconceivable as a fourth-dimensional body is to us.
“The cone would try again. This time, we dip it obliquely. The water now perceives a totally different set of phenomena; there are no circles,
but ellipses. Dip again, first at this angle, then at that. One way we get curious curves called parabolas, the other way equally curious curves called hyperbolas.
“By this time the water would be nearly out of its mind, if it insisted on trying to refer all these absolutely different phenomena to a single cause!
“It might work out a geometry – our own plane geometry, in fact – and it would perhaps get some extraordinary poetic conception of a Creator who manifested in his universe such marvellous and beautiful relations. It would get all sorts of fantastic theories of this Creator’s power; what it would never get – until it produced a James Hinton – would be the idea that all this diversity was caused by seeing, disjointedly, different aspects of one single simple thing.
“I purposely took the easiest case. Suppose that instead of a cone we used an irregular body – the series of impressions would seem to the water like absolute madness!
“Now slide your imagination up one dimension! Do you not see at once how parallel is our situation to that of the surface of the water?
“The first impression of the savage about the universe is of a great mysterious jumble of things which come upon him without rhyme or reason, usually to smite him down.
“Long later, man developed the idea of connecting phenomena, at least a few at a time.
“Centuries elapse; he begins to perceive law, at first operating only in a very few matters.
“More centuries; some bold thinker invents a single cause for all these diverse effects, and calls it God. This hypothesis leads to interminable disputes about the nature of God; in fact, they have never been settled. The problem of the origin of evil, alone, has quite baffled Theology.
“Science advances; we now find that all things are subject to law. There is no need of any mysterious creator, in the old sense; we look for causes in the same order of nature as the effects they produce. We no longer propitiate ghosts to keep our fires alight.
“Now, at last, I and a few others are asking whether the whole universe be not illusion, in exactly the same way as a true surface is an illusion.
“Perhaps the universe is a four-dimensional object, or collection of objects, quite sane, and simple, and intelligible, manifesting itself in diversity, regular or irregular, just as the cone did to the water.”
“Of course I can’t grasp all this; I will ask Cyril to tell me again and again till I do. But what is this fourth-dimensional universe? Can’t you give me something to cling to?”
“Just so. Here this long lecture links up with that little chat about the soul!”
“0– o – oh!”
“And the double personality, and all the rest of it!
“It’s perfectly simple. I, the fourth-dimensional reality, am going about my business in a perfectly legitimate way. I find myself pushing through to my surface, or let us say, I become conscious of my surface, the material universe, much as the cone did as it went through the water. I make my appearance with a yell. I grow. I die. There are the same phenomena of change which we all perceive around us. My three-dimensional mind thinks all this ‘real,’ a history; where at most it is a geography, a partial set of infinite aspects. I say infinite, for the cone contains an infinite number of curves. Yet this three-dimensional being is actually a part of me, though such a minute one; and it rather amuses me, now I have discovered a little bit more of myself, to find that mind think that he, or even his yet baser body, is the one and only.”
“I’m understanding you with a part of me that I didn’t know was there.”
“That’s the way, child. But I’m going on a little. I want you to consider how nicely this explains the psychology of crowds, for example. We may suppose an Idea to be a real four-dimensional thing. I, when I know myself more fully, shall probably turn out to be a pretty simple kind of a thing, manifesting in perhaps one person only. But we can imagine abstract ‘Individuals’ who come to the surface in hundreds or thousands of minds at the same time. Liberty, for example. It begins to push through. It is noticed by one or two men only at first; that is like the point of the cone. Then it spreads gradually – or it breaks out suddenly, just as the circle would, if, instead of a cone, you dropped a spiked shield upon the water. And that is all the lesson for this afternoon, child. Think it over, and see if you have it all clear, and if you can find any other little problems to straighten out. The next lesson will be of a more desperate sort – the kind that leads directly to action.”
Cyril broke in on the word. “We have a great deal to do,” he said sharply, “even before we leave this house. It’s pretty dark – and there’s a Thing in the garden.”
Chapter V
OF THE THING IN THE GARDEN;
AND OF THE WAY OF THE TAO
“OH, little Brother!” said the old mystic sadly.
“How long will it take you to work through this wretched business?”
“I have omnipotence at my command, and eternity at my disposal,” smiled the boy, using Eliphaz Levi’s well-known formula.
“I ought to explain,” said Simple Simon, turning to Lisa. “This boy is a desperate magician confined within the circle of this forest. His plan is Action; he is all for Magick; give him a Wand and a host of Demons to control, and he is happy. For my part, I prefer the Way of the Tao, and to do everything by doing nothing. I know it sounds difficult; one day I will explain. But the practical result is that I lead a placid and contented life, and nothing ever happens; he, on the contrary, makes trouble everywhere, excites the wrath of Turks, and worse, if I am right; he thereby brings about a situation where perfectly competent ladies’ maids have epileptic fits, mediums endeavour to procure blood from bewitching damozels – and now there’s a Thing in the Garden.” His voice had a wail of comic disgust.
“However, this is Cyril’s funeral, not mine. He called me in; I must say I approve of his general plan, on the whole, and I dare say much of the opposition is unavoidable. In any case he is the magician; Principal Boy in a Pantomime. I merely hold the sponge; and we have to use his formula throughout, not mine. If it ends in disaster,” he added as a cheerful afterthought, “perhaps it will teach him a lesson! A Chinese God, indeed! He would be better as a Chinese coolie, smoking opium at the feet of Chwangtze!”
“He tells me that I stand in my own way, that I love struggle and adventure, and that this is weakness and not strength.”
“This girl is in danger: quite unnecessary danger.”
“I am going to ask my master to show you his method; you will see plenty of mine in the next few weeks; and I should like you to have a standard of comparison. Maybe you’ll want to choose one day!”
“I’m afraid I, too, like danger and excitement!” cried Lisa.
“I’m afraid you do! However, since Brother Cyril asks it, the Way of the Tao shall be trodden so far as this is possible: What would Brother Cyril do?”
“I should take the Magic Sword, make the appropriate symbols, and invoke the Names Divine appurtenant thereto: the Thing, shrivelled and blasted, would go back to those that sent it, screaming in agony, cursing at the gods, ready to turn even on its employers, that they might wail with it in torment.”
“One of the best numbers on the programme,” said Simon Iff. “Now see the other way!”
“Yes: if your way is better than that!” cried the girl, her eyes gleaming. “It isn’t my way,” said the mystic, with a sudden inflection of solemnity. His voice rose in a low monotonous chant as he quoted from “The Book of the Heart girt with the Serpent.”
“I, and Me, and Mine were sitting with lutes in the market-place of the great city, the city of the violets and the roses.
“The night fell, and the music of the lutes was stilled.
“The tempest arose, and the music of the lutes was stilled.
“The hour passed, and the music of the lutes was stilled.
“But Thou art E
ternity and Space; Thou art Matter and Motion; and Thou art the Negation of all these things. For there is no symbol of Thee.”
The listeners were thrilled to the marrow of their bones. But the old man merely gathered a handful of dittany leaves from the chased golden box where they were kept, and led the way to the garden.
It was very dark; nothing could be distinguished but the outlines of the shrubs and the line of the fence beyond.
“Do you see the Thing?” said Iff.
Lisa strained her eyes.
“You mustn’t look for anything very definite,” said the mystic.
“It seems as if the darkness were somehow different in that corner,” said Lisa at last, pointing. “A sort of reddish tinge to the murk.”
“Oh dear me! if you will use words hike ‘murk’! I’m afraid you’re all on Cyril’s side! Look now!” And he put his hand on her head. With the other he offered her the dittany. “Chew one of these leaves!” he said.
She took one of the silver-grey heaves, with its delicate snow-bloom, between her teeth.
“I can see a sort of shapeless mass, dark-red,” she said after a pause.
“Now watch!” cried Iff. He took several steps into the garden, and raised his right hand. “Do what thou wilt shall be the whole of the Law!” he proclaimed in such a voice as once shook Sinai.
Then he threw the rest of the dittany in the direction of the Thing.
“By all the powers of the Pentagram!” shouted Cyril Grey; “he’s deliberately making a magical link between it and Lisa.” He bit his lip, and cursed himself in silence; he knew he had been startled out of prudence.
Simon Iff had not noticed the outburst. He quoted “The Book of the Law”, “Be strong!” he cried. “Enjoy all things of sense and rapture! There is no god that shall deny thee for this!”
The Thing became coherent. It contracted slightly. Lisa could now see that it was an animal of the wolf type, couchant. The body was as big as that of a small elephant. It became quite clearly visible. It was a dull fiery red. The head was turned toward her, and she was suddenly shocked to see that it had no eyes.
Diary of a Drug Fiend Page 41