Rock (n.):

a. a large mass of stone. b. a firm foundation or support.

In the rock dwells the dark slumber of the earth (Heidegger, The Thing).

Abyss (n.):

a. what lies below.

b. anything profound, unfathomable, or infinite.

The word for abyss originally means the soil and ground toward which, because it is undermost, a thing tends downward. But in what follows we shall think of the abyss as the complete absence of the ground (Heidegger, What Are Poets For?).

The Thing

We must try and compute life with or without the Black Rock. Anything dark and compact is, in the end, only a specter, an invisible quantity, a rumor hanging in the air which only operates through its subtraction. Filling space with the Black Rock is only meant to show the void that its subtraction leaves. True consistency is the one that cannot be seen. We contrive, in any case, to construct a narrative, and for this reason we couldn’t imagine the Black Rock. It was too dense and too hard to exist in our imagination. But now that it has vanished and pure thought is back, we can perfectly imagine what life without the Black Rock might have consisted of. Precisely, this is consistent; precisely this real future is open to our real speculation, that is to say, to the real future thought that will guide our time.

We never feel more at home in the midst of thought, back in touch with density and consistency, than when we fully assume the duty of thinking, in this case, the duty of narrating the Black Rock merely as an illusion, as a pure play on words, as a mass that had interposed itself in the passage of time only to let time continue its flight without it – only in order that we might weigh up life with or without that mass, and find perfect equality. The path of thinking never appears in a better light than when the specter withdraws. Indeed, the clearing alone is not sufficient; one has to populate it. Precisely, the specter operates like the perfect veil and puts the clearing on hold. It delays it in order, subsequently, to submit it to all the greater unveiling.

Consistency is not made up of homogeneity and continuity. It would crumble if it proceeded alone in time. It requires a succession of specters in order to enumerate the contradictions one after the other. As it progresses, consistency must oscillate from one side of the void to the other, in order to keep track of its line and ceaselessly recover the original meaning after each incident of the specter. Thus, the disappearance of the Black Rock leaves us awake and open in the greater clarity and greater consistency of life without it. On our way to the clearing, we need sounds and vibrations. Precisely, it is a silent explosion that the sudden apparition, then the sudden vanishing, of the Black Rock have produced in space.

We wonder where the traced path was lost and where the illuminated perspective has gone; but we only find, looking ahead, the comforting vibration of space, a sea of tranquility that is only made up of the withdrawing specter. After the specter has withdrawn, we recover the unity and force of the next minute and we find our way again in thought. We keep traversing that interval as the only consistent thing, as the shortest path that keeps opening in front of us, despite its being made up only of randomness and variance. Indeed, the abyss of thought is such that the path cannot be measured metrically. The line admits of no length, and it is a constant deviation that takes its place. Our thought doesn’t traverse a homogenous space but a succession of layers that alternatively produce the Black Rock and conceal it – what is known as the way of the specter – and it is only variance that grows up linearly in time.

It is then tempting to measure the echo of the specter in time. Its appearance and disappearance were only meant, after all, to send tremors into space and to produce, behind our back, what sounds like a song. Although it is a long road ahead of us, we are tempted to reverse our course and entertain a conversation with the specter; we want to express our regrets and recreate the lost opportunity. As a matter of fact, the path of thought is also measured by those volatile words. And the long conversation with the specter is even less linear than the path of thought through time. It, too, is measured by gaps and eruptions.

After the Black Rock has vanished, after the dark and compact mass has moved out of the way, the only thing left is the music of time, a sign of the recognition of thought – or rather, its song. In the sea we are traversing, thought is indeed the only siren. It helps us navigate better than any specter, and our whole future and past, all that constitutes our path, soon appears as its sole property and its sole effect. The perpetual oscillation of the specter, the question of life with or without it, is to our siren, merely a singing exercise.

The Abyss

What could be the purpose of imagining all those worlds and, moreover, of imagining how big they are? What is realer and more consistent? The world in which we imagine we could have lived with the Black Rock, or the reality of its disappearance, which is essentially the proof of our consistency? We should even try and imagine a constructive proof of the latter. Although the essence of our enterprise may be elusive, although we may not be able to spell out exactly the concrete trials that await us or to say, ahead of time, how subtle and exclusive our advance will be, we can gain the precision we need, and our proof will be consistent, if we make the random variables converge. The strong law of large numbers is the only certainty and the only evidence of matter. It is by letting the random variables follow each other in a sequence – together with all the contradictions that constitute the voice of the specter – that the strong law of large numbers establishes the matter and the consistency of our enterprise.

There is no better way of constructing our proof of thought than to advance, as we do, in what looks like the void but is in reality only constituted of a large number of contradictions and oscillations, of a converging sequence that is not grounded in numbers but that obtains, at every step, by virtue of the infinite intensity of the abyss. In this, we come to realize that the faces of the die we are rolling, or generally numbers that we see produced, do not exist as such. They don’t vibrate or produce music or anything coming from the depth; they don’t produce anything proper to the siren or anything that might help thought progress on its path. Numbers as such do not converge. For the number to exist and the face to converge (and that which converges is that which exists), the abyss has to open behind the face and the face has to be correlated with a random trial.

The world that selects the face and makes it exist is the one that makes it vibrate. This is the world that says that the die has been thrown and trialed, that the face has presented itself, only the face could have been different. Reality is not the reality of the face or the image. To be sure, we mention the reality that lets us advance at every step, the reality we call present and manifest like the face of the die; however, this reality cannot support the reality of our thought. Manifest reality cannot help us progress in thought; it cannot help us construct the proof of our thought unless it “converges.” To that effect, it needs to be supported, subtended, by the infinity that is contained in the abyss and in each concrete trial.

Thus, thought is never independent of matter. The constructive proof of thought is obtained by turning matter into liquid, that is to say, by making time equal to money. The abyss that lies underneath the face can turn it into a space for thought and into a path – keeping in mind that the only space of thought is time – only if it springs forward and presents thought with a new matter. This is a matter that condenses the intensity of the bottomless abyss and virtually places it in each step that thought takes forward. Within the path of thought, within the line that thought must traverse in time and that is only constituted of the oscillations of the specter, it is, thus, the whole world that keeps springing out in a remarkable inversion. Volatility is the only guarantee that matter exists and that thought is being constructed, and the oscillation between the appearance and the disappearance of the Black Rock keeps increasing in frequency to the point where infinity becomes contained in a single instant. For thought that now stands on that instant as solidly as it would on a rock, this infinite volatility is even better than a proof of the world springing out of the abyss. It is the concrete trial of the world.

The music of our thought has reached the degree of refinement that makes the world spring forth at each one of our steps. It is entirely up to us to recognize, in that song, the unique constructive proof of our thought and not to yield to illusion or to imagination. Our thought is real and is the absolute opposite of illusion – it is precisely opposite to all the imagined worlds, no matter how big they are – because it rests on their infinite vibration. Randomness is bottomless, and it doesn’t belong to us to decide the world in which the Black Rock will be or not be. What is proper to us and to our thought is the reality of the construction, or the reality of language. It is the calculus of the events, also known as the algebra of events. This continual abstraction must be given the solidity and the firmness of the concrete. Presumably, this is made possible by the inversion that characterizes the derivatives market and, generally, writing. Indeed, writing is what turns into liquid the depth of the abyss and its black color.

"Abyss", Fortuné Penniman, dzięki uprzejmości artysty.

The Dust

How to get rid of the Black Rock? How to choose between two products of the imagination: the future world that doesn’t exist and is merely tempting us and attracting us, and thought which constitutes itself into a reality by the sheer power of abstraction, by the extraction of the infinity of the abyss under each step that it takes? Yes, the reality of thought is no less imaginary than that of the non-existent world. Yes, thought is imagination. However, its reality has the advantage of being proper to it. It is constructed at every step. In the end, it is all a matter of properly configuring time. Let us then rephrase our proposition and say that a new order of time has emerged and has categorized the infinity of the concrete abyss. This new order is then simply equal to the order of thought. Presumably, the oscillations and contradictions that were witnessed were simply those of time and one has simply to choose between two configurations of time: the constructive path of thinking or the chaotic infinity of the abyss.

Lately, a single question has been on our mind and has marked the rhythm of our thought: “Will the Black Rock make contact with us again, and if so, when?” The time has come, however, to recognize this question as a pure illusion and to see the construction lying behind it as only reality. This construction is properly that of time. Once the construction of time is mastered – and this is what we are constantly striving for, through the sustained oscillation of our writing – it won’t matter anymore whether the abysmal world underlying it is populated by the largest or by the smallest mass, by the Black Rock or by its complete pulverization into an infinity of particles of dust. Soon enough, in the time that is thus constructed, only the song of the siren will be heard – a song that will be proper to us, this time, and will originate from no other place than our head, a song that will no longer require that our ears be sealed. Better than a song, it will be music, a sea of tranquility for the thought that was able to invert the chaos and the infinity of the abyss.

We will be rid of the Black Rock after we turn the strident oscillation of its mass perfectly into music, after the whole question of its appearance or disappearance and our whole oscillation between the world in which it exists, and the world in which it doesn’t, converge into one shrinking interval and one elementary step of thought. This is when the alarm call, the strident siren, gets transformed into a musical note. To the Black Rock that imagines itself as massive as the world, we show that its fatidic oscillation has, on the contrary, helped us master what is subtlest and finest, namely the minute of time, the next minute that clashes with the world in which the Black Rock is imagined and makes it imaginary, precisely. The world is strident and abysmal, but the next minute becomes musical as soon as it is constructed by thought. The construction doesn’t consist in sealing our ears, but in constituting the sea, then the vessel, then the mast against which we remain tied while we listen to the song.

To the Black Rock we give every assurance that we will never forget it and that we will not obliterate the world in which it could exist. To the contrary, we now forge this world in our own way; we stamp it on the reverse side of the real world and we let their oscillation converge within the single instant of our thought. We properly create matter through the strong law of this convergence and we mint this coin as unity itself – as the deepest and best-grounded unity we could finally lend to our time. To the Black Rock we answer that we have transformed – that we have literally transmuted – its imaginary and even unimaginable world into the reality of our time and the harmony of our melody. As a consequence, the Black Rock is no longer an illusion or a product of our imagination but becomes a true element of our thought. We could almost summon it to the constitution of other times, just for the sake of casting our ship toward other horizons.

We will never forget the Black Rock, because in every future adventure and every future journey of thought, in every future odyssey of time, there will be present the oscillation and recognizable ring of the Black Rock – that is to say, the thoughtful moment that its abysmal and strident world has occasioned for us.

If we master time, then we master the explosion. The minute of time is made of nothing but the explosion, and dust is what best occupies space and time. The power that the explosion of the Black Rock has helped us master is, in the end, equal to the power of thought, which is equal to the power of time. Thus, we have acquired the power to reverse time. We have built a bridge and we have walked over the abyss. The world of the Black Rock has become part of the matter of our thought, that is to say, part of its bedrock and of its past. If the Black Rock ever makes contact with us again, we shall answer it with a song.

"The Rock", Fortuné Penniman, dzięki uprzejmości artysty.

The Poets

Armed with the power of time and with a mastery now guaranteed by chemical forces, do we have the possibility or, even before that, the ambition to create an industry? If matter was created by imprinting the Black Rock and its loss on either side of our coin, as the two faces that build for our thought precisely the bridge of probability and expectation, precisely the rigor and patience whose other name is measure, will we be able to perpetuate this matter? If the Black Rock and its loss are the two faces of reality that construct our thought and help it lay a firm foot over the abyss through their oscillation, will we be able to transform this matter into a real industry?

What could the industry of the minute be, compared to the massive concreteness of the world? What could the music be, which would give meaning to the stridency of the split (the world with or without the Black Rock) and print it in memory? What could the composition be, in which the massive oscillation of the Black Rock would be nothing more than a musical reminiscence, or only a theme? Is it fair to conclude that our industry is the industry of expectation, and our matter the matter of time?

We’ve always entertained the thought that the derivative pricing industry in which we are engaged is a refinement of matter and even a writing style, and that any other industry which has chosen the future and contingency as its raw material will eventually compete with ours in the degree of refinement and the beauty of style. But now, after the reconfiguration of time and the transformation of the Black Rock into musical dust, we come to understand that our two industries were never comparable and never shared the same world.

It is truly the incompatibility of registers and of logical categories that prevents an enterprise like ours from striking a deal or even establishing a link with the Black Rock that has hurled itself so massively in the abyss. Consequently, it is not a mystery that the Black Rock should vanish, and its loss should not disquiet our thought. It is simply that our musical world has taken the lead. Enough that we recover the refinement and the rigor of our pricing technology, and the world will be one in which the Black Rock has turned into dust.

As always, the greatest difficulty lies in the separation of the registers of time. Time is the reciprocal of the abyss. Whereas all things fall in the abyss and get dispersed into its infinite detail; whereas things get stopped, as they fall into the abyss, at innumerably different levels and heights, time, on the contrary, seems to give them back some unity; it lends them the unique passage of time. Time is the abyss without depth, the abyss turned horizontal in which all things seem to pass at once, and mix with each other. Thus, the Black Rock and we have met in time and entertained a conversation for a while. The difficulty, however, consists in verifying – indeed, in concluding – that our dialogue was only made of discordancy and that, although they seemed to follow each other, none of the words we said followed from the previous one and respected its order.

Our industry is the one that untangles the strands of the incompatible worlds and finds music inside the noise, or worse, inside the stridence. We have learnt the language and constructed the time in which we are finally able to say that the Black Rock indeed doesn’t exist but could have existed on the other face of the world we are holding in our hand, or before our eyes.

We use the dust from the Black Rock to manufacture kohl, or the black ink with which we accentuate our eyes. We project before our eyes the line that they can follow; we simply write the music that we will listen to again in peace.

Our industry consists in putting back the colossal world inside the urn and in making the stridence of the chaos fit again inside the musical note. We meet the world with the degree of refinement of derivative pricing, and as a result we are able to walk on the volatility surfaces. This expression alone, if it were analyzed, would suffice to show the incompatibility between our industry and the Black Rock. In the world of the Black Rock, our music is only made of silence and this piece is only made of dust.


Elie Ayache was born in Lebanon in 1966. He was trained as an engineer at lÉcole Polytechnique of Paris and he pursued a career of option market-maker on the floor of MATIF (19871990) and LIFFE (19901995). He then turned to the philosophy of probability by earning a DEA at la Sorbonne. In 1999, he co-founded ITO 33, a financial software company, specialized in derivative pricing technology. Today, ITO 33 is the leading specialist in the pricing of convertible bonds, in the equity-to-credit problem, and more generally in the calibration and recalibration of volatility surfaces. Ayache has published numerous articles on the philosophy of contingent claims. He is the author of The Blank Swan: The End of Probability (2010), and of The Medium of Contingency: An Inverse View of the Market (2015).

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