LUNCH, AFTER ALL; AND A LUMINOUS ACCOUNT OF THE FOURTH DIMENSION
“I CONFESS to hunger,” said Simon Iff, after a few moments. Cyril kissed Lisa on the mouth, and walked with his arm still circling her, to the sideboard. “You are hostess here now you know,” he said quite simply. All his affectations dropped from him at that moment, and Lisa understood that he was just a simple-minded, brave, and honest man, who, walking in the midst of perils, had devised a formidable armament both for attack and defence.
She felt a curious pang of pain simultaneously with a sense of exaltation. For she was no longer merely his mistress; he had accepted her as a friend. It was no longer a purely sexual relation, which is always in the nature of a duel; he might cease to love her, in the crude savage sense; but he would always be a pal – just as if she were a man. And here was the pang: was he sure to return to the mood that her whole body and soul were even at that moment crying out for?
The story of his “Judgment of Paris,” as they called it, came into her mind. Some years before, he had had three women in love with him at once. It seemed to each that she was the only one. But they discovered the arrangement – he never took pains to hide such things – and they agreed to confront him. They called at his studio together, and  told him that he must choose one of them. He smoked a full pipe before replying; then went to his bedroom and returned with a pair of socks – in need of attention. “Simon, Son of Jonas, lovest thou me? – Yea, Lord, thou knowest that I love thee. Mend my socks,” he misquoted somewhat blasphemously, and threw the socks to the one he really loved.
Lisa meant to lay the table in that sense of the word, so to speak. She remembered that the only words spoken by Kundry after her redemption were “Dienen! Dienen!”
“Is this your fast? ” she cried gaily, discovering the contents of the sideboard. For her gaze fell upon a lobster salad of surprising glory flanked by a bowl of caviar in ice on one side, and one of those foie gras pies – the only kind really worth eating – which you have to cut with a spoon dipped in hot water. On an upper shelf was a pyramid of woodcock, prepared for the chafing dish which stood beside them; there was a basket of pears and grapes of more value than a virtuous woman – and we know that her price is above rubies! In the background stood the wines in cohorts. There was hock from the cellars of Prince Metternich; there was Burgundy – a Chambertin that could have given body to a ghost, and hardly lost its potency; there was a Tokay that really was Imperial; there was 1865 brandy made him 1865 – which is as rare as radium in pitchblende.
Simon Iff took it upon himself to explain his apparent lack of hospitality toward the visitors.
“Akbar Pasha came here for blood: a drop of your blood, my dear; Cyril's and mine are not in his power – you saw how contemptuously the boy played up to his trick! So I persisted in offering him salt, and nothing but salt.” 
“But why should he want my blood? And why should you give him salt?”
“If he accepts salt it limits his powers to injure the house where he accepts it, or its inmates; and it exposes him to a terrible riposte. Why he should want your blood – that is another question, and a very serious one. Unfortunately, it implies that he knows who you are, and what we purpose for you. If he had it, he could influence you to do his will; we only wish that you should be free to do your own. I won't insult you by telling you that you can go scatheless by the simple process of returning to your ordinary life. I've been watching you, and I know you would despise me for suggesting it. I know that you are ignorant of what may lie before you, but that you judge it to be formidable; and that you embrace the adventure with both hands.”
“I mustn't contradict time famous expert in psychology!” she laughed back at him. “I ought to deny it indignantly. And I surely am crazy to leap in the dark – only it isn't dark when Love is the lamp.”
“Be careful of love!” the old magician warned her. “Love is a Jack o' Lantern, and hovers over bogs and graves; it's but a luminous bubble of poisonous gas. In our Order we say 'Love is the law, love under will.' Will is the iron signal staff. Fix love on that, and you have a lighthouse, and your ship comes safe to harbour!”
“ I may now apologize,” remarked Cyril, as they seated themselves at the table, “for leaving you the other night to dine at Miss Badger's. I had given my word to her, and nothing but physical inability would have stopped me from going. I didn't want to go, any more than I wanted to drown myself; and that is a great compliment to you, for she is one of the two nicest women in London; but I would have faced a thousand deaths to get there.” 
“It is right to be so stern about a trifle?”
“Keeping one's word is no trifle. False in one, false in all. Can't you see how simple it makes life for me, never to have to worry about a decision, always to be able to refer everything to a simple standard, my Will? And can't you see how simple it makes life for you, to know that if I once say a thing, I'll do it?”
“Yes. I do see. But, oh, Cyril, what agony I passed through that evening!”
“That was ignorance,” said Simon Iff, “the cause of all suffering. You failed to read him, to be assured that, just as he was keeping his word to Miss Badger about the dinner, he would keep his to you about the telephone.”
“Now, tell me about the Battle. I see that I am in the thick of the fight; but I haven't got a ghost of a notion why!”
“I'm sorry, dear child, but this Knowledge is unsuited to your exalted grade,” he answered playfully. “We must get up to it slowly by telling you exactly what we want to do, and why. Then you will see why others should try to thwart us. And I deeply regret to have to inform you that our road lies through somewhat hilly country. You will have to listen to a lecture on the Fourth Dimension.”
“Whatever in the world is that?”
“I think we had better talk of simpler matters until hunch is over.”
They began to discuss their private affairs. There was no reason at all why Lisa should not take up her residence with Cyril from that moment. She had merely to telephone her maid to pack, and come along. She offered to do so when Simon Iff said that he thought they ought to leave Paris without a day's delay. But he said: “I don't think it quite fair on the girl. It's a battle, and no call for her to  fight. Besides” – he turned to Cyril – “she would probably be obsessed in twenty-four hours.”
I shouldn't be surprised to learn that they were after her already. Let's try! Call her, Lisa, and say you'll not be back to-night; tell her to wait further instructions.“
Lisa went to the telephone. Instead of getting her room, she was connected with the manager of the hotel. “I much regret to have to tell you, madame, that your maid was seized with epileptic fits shortly after you left this morning.”
Lisa was too stunned to reply. She dropped the receiver. Cyril crossed to her instantly, and told the man that his news had upset Madame; she would telephone again later.
Lisa repeated what the manager had said.
“I thought as much,” said Cyril.
“I didn't,” said Iff frankly, “and it worries me. I'm not guessing, like you are – and it's no credit to guess right, my young friend, but a deceit of the devil, like winning at roulette. I'm deducing from what I know. Therefore, the fact that I'm wrong proves that there is something I don't know – and it worries me. But, clearly, we must get into a properly protected area without a moment wasted. That is, you must. I'll watch at the front. There must be somebody big behind that clumsy fool Akbar Pasha.”
“Yes; I've been guessing,” admitted Cyril, with some shame. “Or, perhaps worse, I've let my ego expand, and taken the largest possible view of the importance of our project.”
“Well, tell me the project!” said Lisa. “Can't you see I can hardly bear this any more?”
“You're safe within these walls,” said Simon, “now that there is no enemy within the gates; and to-night we shall take you under guard to a protected area. To-morrow the fun will begin in  good earnest. Meanwhile, here is the preliminary knowledge with regard to the project. Before you start, you have to take a certain vow; and we cannot allow you to do that in ignorance of all that it implies, down to the tiniest iota.”
“I am ready.”
“I am going to make everything as simple as I possibly can. You have a good imagination, and I think you should be able to follow.
“See here: I take a pencil and a piece of paper. I make a point. It stays there. It doesn't go in any direction. In mathematics we say: 'It is extended in no dimension.' Now I draw a straight line. That goes in one direction. We say, it is extended in one dimension.
“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.”
“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.”
“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.'”
“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.”
“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 it, (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 realize,” 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 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?”
“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 rime 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 lounger 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!”
“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.” 
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