“The connection between the symbol and the symbolised? What on earth are you talking about?” I replied with a haughty indignation. P looked back with mild disgust. “I know it will be hard for you to understand, but this is why you must listen with special attention. Only through such an attention will you grasp what I will tell you.” P managed to put enough dramatic import into his speech such that it arrested me. “Go on.” I said, trying to look attentive. “When we symbolise something we draw a line between thing and symbol.” “Is that it?” “Is that not enough?” “It doesn’t sound much?” “Do you accept it?” I thought for a moment. “No” I replied “Of course not, there might be all manner of different symbols for the same thing. No connecting line is needed.” “Then you do not understand, for this is simply the naive understanding spat back at me.” I became indignant “P, this is something of an outrageous notion. I am not the one with naive understanding. The notion of symbolic connection to the symbolised itself is the primitive mode of thought. It is this that is the naivety and the recognition of the arbitrariness that is the more advanced mode of thought.” P looked unruffled “You are right of course.” There was a hiatus of several seconds. “Do you know the science of dialectics?” I wanted to reply that dialectics was not a science but instead merely grunted an assent “Then you will understand how what I tell you is a sublation of the original state that has moved beyond its naivete.” He paused as if this was sufficient and I felt I must point out the inadequacy that I perceived “P it is not enough simply to say a ‘sublation’ has taken place, I feel I must know how this original naivete has been rehabilitated in order to feel any satisfaction from you explanation, which in truth is not really an explanation yet.” P sighed heavily and began again “Always I must break everything down. I warn you, in forcing me to break it down you may render then thing I seek to explain impossible to do so. I will try for I am not afraid of the effort, I would however rather that it was you and not I that made this effort. I feel for myself I have already been perfectly clear, yet your incessant badgering has forced me to make a more thorough explanation, an explanation which will potentially be more unclear than the the short version. If this occurs you will at least know you have only yourself to blame.” I refused to rise to this and waited for the explanation, which I felt really was a perfectly reasonable to ask for. P continued “Initially we were wont to think that symbol and symbolised, word and object were connected. As you point out, we observed that this is an arbitrary relation with no ground to it. This gave rise to the picture that asserted the opposite: the symbol contains no relation to the symbolised. Even if there is semblance it does not matter, the two are disconnected. Finally I came to understand that this too was insufficient as it has ruled out the possibility that their is a connection in the power of the mind. The second stage presupposes there is no power. But if we reinstate this power then, yes the connection is arbitrary, yet once formed it is however real.” I looked on with mild interest. “This is quite interesting P, but it does rather turn on your ‘power of the mind’ being real. If this power is not real, your point collapses somewhat does it not?” “My point does not collapse any more than the point of someone who originally pointed out the arbitrariness of the connection. They merely proffered that the two are not be connected because the connection is so absurd. The absurdity was accepted and the connection rejected. However by reducing the claim only to the power of the mind -something that remains a reasonable possibility- we can reintegrate the connection, just on a slightly less necessary footing.” I felt I had partially lost the thread but did not wish to convey this. Incapable of making a proper assessment of P’s claim I foundered “I see” I said. P pounced “You do not see, you entirely fail to see.Fortunately for you this was only to be expected. You do not have the insight that was supplied to me. This has been obscured because we have strayed from the point.” “And what is the point?” “The point is that the number relates directly to the relation between the symbol and the symbolised.” “Oh” I said, and leaned in to listen with greater attention. “As we know, an empirical proof is always the most impressive.” I nodded “Fortunately this number supplies exactly this proof.” P paused, then continued “Do you know what numbers are?” “Numbers are the system we use to count the objects in the world. The base is arbitrary and their absolute nature unknown.” “A classic an concise answer, however hopelessly misguided. Numbers are doors.” “Numbers are doors?” “Yes numbers are doors, or maybe openings is better” He seemed to lose some of his poetic force, it seemed appropriate to interject “So are they the doors or the doorways?” “I suppose I can stay with my initial statement that they are doors? Can you knock on them?” P gave my facetious statement a stare “I suppose in a sense you can. Though maybe no one will answer and you will have to open the door yourself. I am not sure if there is a metaphorical counterpart to ‘knocking’…” P stopped and was clearly pondering this matter. Annoyed with the manner in which my gesture had backfired, I attempted to move P onwards “So you were saying how numbers are like doors.” “Yes, numbers are like doors, when you knock on them they sometimes open and you may go through. Though note I say ‘go through’ and not ‘go inside’, for ‘going inside’ is not an option, whereas ‘going through’ is the only option, unless of course one declines to ‘go through’. This option though seems rather pointless since the door will have only opened if you have knocked, hence to not go through would be almost rude.” “But how does one go through?” “One goes through in the way one goes through a doorway, since as mentioned numbers are akin to such things.” “But if we must make actual sense of what you mean, what does going through mean, let’s say to you in the case of this number you have derived from J?” “Well it is a kind of investigating.” “What kind of investigating?” “It is a kind of investigating in which no relation is off limits.” “Go on.” “So in the case of this number, it is made of two separate integers. So following a well known occult practice the most obvious thing to do would be to check each of these numbers separately as to what their highest incarnations might be?” “I’m sorry? Their what?” “Highest incarnations.” “And how do we do that?” “We simply use the water and earthen paths of numbers. To water a number we simply multiply it by itself, this gives us its swollen self. So the first part of this number is 4, which watered is 16. Then comes the earthen or telluric operation. Since earth stands in solid blocks so we must stack the numbers together, hence we add the 1 to the 6 giving us 7.” “Is that it?” “No, for we do not yet know if we have reached the highest point. We must reapply the watery path. This will give us 49, to which we then apply the telluric formula.” “13?” “Yes, though we must do the same thing again, hence we reach 4… again.” He paused for a dramatic effect, I was not impressed and he perceived this “I think maybe you have not grasped it properly yet, through these operations, which I myself did not invent, the 4 has become 7 and the 7 has become 4. I have gone through the number and found a hall of mirrors, a hall of infinite 4s and 7s!” “I will grant you that it is quite neat, but I am not sure of its relevance to the matter of the symbol and the symbolised.” “I did warn you this was a long and complicated process, had you simply accepted the pithy version that I offered earlier, you would not now be struggling so hard. I said earlier that we must interrogate the number for any relations possible. When we consider the angular nature of 4 and 7 we find there is a strong resemblance is there not?” “I’m sorry P, what do you mean? The angular nature of 4 and 7? Do you mean if we divide a circle into 4 and into 7 there is some relation in the resulting angles?” P look momentarily flustered but restored himself swiftly “No, not in that way. The symbols, if we look at the symbols for 4 and 7 we find there is some angular similarity. Look…” he dragged a crumpled piece of paper from his pocket and sketched a 4 and a 7 upon it “…see, there is a kind of upside 7 in the 4 and a diagonal one.” “You mean in the symbol then, and not in the number” I retorted “We must assume, as in a conditional proof, that the two are connected in order to see the connection, you assent at least to some symbolic similarity?” I mumbled a kind of agreement, though I felt it only slightly “Then you will agree also that both of them have some relation to the triangle.” He sketched again, adding the extra line to the 7 to form a triangle and showing the triangle that formed the 4, I could only nod. “Since they both are related to triangles we must assume that the patterns we find in their oscillating repetition also are related to triangles. But how?” P looked very pleased with himself “You are going to tell me I feel sure.” “I am going to tell you, you are correct. You must imagine a triangle made of units.” “I can imagine such a thing.” “The triangle must be made of units such that the point is 1 unit and the next line is 3 units, the next 5 units and so on.” I nodded that I followed him. “Now observe this truth. If we have have a triangle of 4 units in height, how many will be on the base?” I thought for a moment then answered “7” P grinned, but I did not rise to this “If you have a triangle of 7 units in height, how many units will you have on the base?” Again I paused, then replied “13” “Remember how we must apply to motion of earth to such numbers!” “And what was that again? To multiply it by itself?” “No! That was the motion of water! The motion of earth was to solidify the numbers together, which would give us…?” “4” I conceded, secretly a little bit impressed “Yes 4! Now maybe you see! This precious oscillating number gives us the bridge. It is the door that shows the connection between symbol and symbolised!” “This is maybe a bit strong P. The triangular connection may have been how you got the insight, but to make the connection necessary seems a little strained.” P did not seem to be listening “That is not the only seemingly arbitrary relation that has been disproved here. Have you noticed anything else especial about what you have seen?” I replied that I had not “Consider that the base that we work, base 10 as we call it. Did you not yourself earlier note that it is essentially arbitrary?” “Yes, how can it be otherwise, without invoking some kind of divine fiat that gave us this number base over others -meaning previous civilisations were actually wrong, which would be an absurdity.” “This is all true. And yet, what I have shown you would seem to indicate otherwise.” “In what way?” “Well is a triangle in a base?” “No, its relations can be calculated in any base.” “Yet what I showed you was based on the units of a kind of a triangle. Regardless of the base 4 and 7 were connected. Even if they were no longer called 4 and 7 and were in some totally alien system, in this unit based geometry, in that triangle formed in that way, which was intimated to me by the chance shape of the symbols, they are related. I created neither symbol nor unit based triangle and yet the relation is there! Now do you see.” “Yes I see.” I replied, though in truth I was not really convinced.