## What is Additivism? (part I of II)

Just watch this video, like I have 4 or 5 times, and ask yourself the question “what is additivism?”

The student of nonlinear dynamics immediately thinks of additivism as a conservative concept.

In a linear system, the total effect of the combined action of two or more operations is merely the additive superposition of the effects of each operation individually. So where additivism prevails, the principle of superposition holds, and the system in turn is restricted to a graduated, quantitatively lower or higher behavior, but at any rate is always qualitatively the same, it remains unchanged, viz. a change by degrees that does not produce a new change in kind.  And as Ed Lorenz often liked to observe, linear systems have two choices: they either remain locally-bound or they fly off to infinity.

By contrast, in a nonlinear system, the combined effect of two or more elementary operations can induce dramatic effects, disposing the system of new solutions whose availability were previously latent or unactualized. Here one observes perhaps even an incremental change by degrees, but which suddenly produces a new change in kind. The divergent evolutionary process of difference by way of repetition, topological folding and twisting, nonorientability -these are all the kinds of system-behaviors cooked into nonlinearity.

My sense is, after watching the video, thinking (which I like to do sometimes), and reading up on their cookbook project, that Additivism self-understands itself to be wagering on nonlinearity -and yet there’s that term, “additivism”.

So my question is, what, prey-tell (that’s not a typo -come on people let’s distribute a new meme!), is additivism?

## Exotic Options as Smart Contracts

“Get out of the sun or you’ll die!”, cried the Lizard, “there are only two possible options, here!”

“Not for me”, replied the Mammal, “evolution has written me a new possibility –I can regulate my internal body temperature.”

“How is this possible?” asked the Lizard, marveling at the notion that what was once impossible for all animals was now possible for the Mammal.

“Well, I’m not exactly sure”, answered the Mammal, truthfully.

“I know how”, offered the biologist.

The two animals turned towards her…

There are persons, including us here at Specmat, who find themselves compelled to think-on and tinker-with second generation blockchain capacities. They share in common the ‘sense’ that combining the algorithmic art of cryptography with digitally-distributed public networks now enables us to write new protocols, which secure new kinds of relationships, whose endogenous capacities greatly exceed the limits of what was previously possible. It’s not so much that smart contracts written on a blockchain to create distributed applications (Dapps) now awaken us to new possibilities, as it is the case that these technologies have actualized a new set of possibilities which were previously nonexistent, and it is therefore up to us to awaken to, examine, and understand this fact, in order to think-on and tinker-with, and deploy their powers.

Nick Szabo, so far as I can tell, coined the term ‘smart contracts’. In his classic essay on the topic, he defines them: ‘Smart contracts utilize protocols and user interfaces to facilitate all steps of the contracting process…The basic idea behind smart contracts is [thus] that many kinds of contractual clauses (such as collateral, bonding, delineation of property rights, etc.) can be embedded in hardware and software we deal with…’[1] This seductively simple notion has profound capacities when deployed on a digitally-distributed public ledger, called a blockchain. In fact, whether Nick Szabo is or is not Satoshi Nakamoto is probably beside the point at this time. We’re currently witnessing the progressive differentiation of an era of second generation blockchain technology, wherein Ethereum and Eris Industries, among others, are developing and enjoining us to develop with them the unbounded number of new protocols which smart contract-enabled Dapps on a blockchain make possible. And here at SpecMat, as we’ve said before, we believe nothing is more suitably commensurate with the wagers of second generation blockchain technology than the second generation options technology called exotic options.

Let us evaluate this claim.

Channing starts a goodserv

Channing believes she has a good idea for a start-up goodserv.

The first thing Channing must do is publicize her goodserv’s existence. She does this by registering her goodserv’s name and product with some Dapp, whose protocol is a distributed name registration database (a kind of Namecoin-equivalent), to which any first-to-file registrant who wishes to start-up a goodserv can go to register her goodserv’s name and product.

Channing registers her goodserv on this Dapp. Now Channing’s goodserv has been made public on blockchain.

The next thing Channing wants to do is fund her start-up. She needs to raise some funds to get things going. The most common method of raising funds is to take out a loan, or some other form of debt (e.g. a bond, a note, some commercial paper). But she’s reluctant to ‘go into’ debt to do so, since she knows this indefinitely indebts her goodserv’s unknown future market value to its present notional value, which is currently at zero. The other common method of getting seed money is to issue equity, so this is what she wants to do; but given the fact that Channing can’t issue ‘stock’ in a goodserv that doesn’t yet exist, and even if she could, she doesn’t want a set of sedentary ‘shareholders’ extracting the future surplus from her goodserv’s net profits, but rather would prefer to enfranchise ‘stakeholders’ working with her towards the mutual, shared success of their common venture –which is, namely, Channing’s goodserv. This means that Channing, in other words, is both aesthetically- and philosophically-disinclined to issue stock, so she will not be selling stock in her goodserv at this time.

What else can she do? How can she fund her start-up costs?

The answer is, Channing will write and sell exotic options. And she will use the cash from their sale to fund the start-up of her goodserv.

Writing Optionality

Exotic options are a second generation class of options. Options comprise a class of financial derivatives. Financial derivatives comprise a class of financial assets. Financial assets are commodities that can be bought and sold like anything else. The difference, however, is that anyone can write an option ex nihilo into existence, without having to first own anything whatsoever. To write and sell an option is simply to create and sell for a fee optionality to someone else; and to buy and hold an option gives its holder optionality.

There are two kinds of options. There are ‘call options’, the holding of which gives one the right to acquire something for a certain pre-agreed to price (called the ‘strike price’ K), on or by a future date (called ‘maturity’ or ‘expiration’). And there are ‘put options’, the holding of which gives one the right to part with something for a strike price K on or by expiration. Common financial markets practice is such that this ‘something’ which the call/put holder has bought the right to acquire/part-with is a stock, or some other standardized financial asset. Let us include this notion, but also broaden its scope of possible objects so as to include anything produced by a goodserv.

We have said Channing is going to fund her start-up by writing and selling exotic options. She is therefore someone who ‘operators’ optionality. She is writing optionality. She is creating optionality ex nihilo, and potentially ad infinitum (though this latter phrase, of course, is just a manner of speaking).

Operators are persons who write and sell, and buy and read options. Operators trade optionality. An operator will therefore need to keep a ‘book’, which houses her total portfolio of assets and liabilities: it will contain options which are written and sold (liabilities) and options which are held and may be read (assets), as well as any synthetic assets, cash-currencies, and any referent assets. These contents of an operator’s book are stored at a digital address, which is secured and managed by a smart contract on blockchain.

There are two types of operators, ‘writers’ and ‘readers’; and two types of operations, writing and reading. To write optionality is to compose and issue an option for a premium price to a reader, who now holds the right to choose to acquire some pre-agreed to asset A, whether an object, amount, or service, at a predetermined price K, if mutually pre-agreed-to conditions are met at maturity and/or during the life of the option. To read optionality is to acquire an option for a premium price from a writer, who now accepts liability to deliver some pre-agreed to asset A, whether an object, amount, or service, at a predetermined price to the reader, if mutually pre-agreed-to conditions are met at maturity and/or during the life of the option. For this reason we can see that writers issue optionality for a premium fee, and accept liability if conditions written into the option contract are met; and readers accept optionality, and pay a premium fee for the right to read optionality, thus exercising their optionality if conditions written into the option contract are met. We label the premium price of a call option C, and the premium price of a put option P.

In life, everyone wants options. The state of having options is called optionality. Options are a financial technology for creating and selling optionality. And operators on a blockchain can now write and read options, and will be constantly reading and writing optionality anew.

What we have just said equally applies to exotic options or vanilla options; these are the two classes of options. Vanillas are standardized, and conventionally-structured, and it is true that today ‘anyone’ can trade them, even without a blockchain, smart contracts, or Dapps. For example, today if you were to register (for a fee) in order to apply (for a fee) for an options account (on which you pay a fee) to begin trading options (for a fee) on one the many options brokerage houses, you will most likely only be buying and selling vanilla options (for a fee), and will not have the opportunity to write or read exotics (or if you are able to, there’s a big fee you’re charged). Exotics are bespoke, customizable, and have unconventional structures. And if managed by a Dapp as a series of smart contracts on a blockchain, there would be little-to-no cost for anyone to begin writing and reading options. You’d also immediately have a distributed space, with a self-authenticating, secure public ledger, which would be nothing less than (but also more than!) an autonomous space for transactions that is presently known and defined as a ‘market’.

Exotics as Smart Contracts on Blockchain

So let us first understand these two terms, ‘smart contracts’ and ‘blockchain’, and then we’ll consider their use-value for Channing’s attempt to fund her start-up with without indebting herself, but rather by writing and selling for a fee some optionality on her start-up’s future value.

The most general acceptable definition of a smart contract is a user-agreed-to customizable rule or set of rules which governs case-specific interactions of the users of a blockchain. These interactions, like all interactions in life, produce and are comprised of arbitrary data.

The most general acceptable definition of a blockchain is a digitally-distributed space for the time-stamped storage of arbitrary data.

Like many profound technologies, both of these things sound remarkably simple, and in truth they are: the ‘arbitrary data’ stored on a blockchain could be the content and terms of an economic transaction between two or more parties, the amount of money in an account, the results of casting and tallying votes, or any other arbitrary data that one can imagine, or that two or more people might produce, or require to govern their interactions.

However, when the distributed technology of a blockchain is combined with the hyperflexible, fully-customizable technology of smart contracts, all of the blockchain’s opt-in users are immediately equipped with an interminable, modifiable, secure mechanism to convene, deliberate, vote, and implement agreed-to rules and permissions to create and modify data, through a set of self-administering and self-executing scripts. And these scripts can literally be anything, their potential is unbounded: any user-agreed-to consensus or security rules can be used to manage the blockchain. Once they’re written and agreed to, the scripts are then time-stamped, executed, and publicly registered on the blockchain. They are smart contracts.

Ok, fine. So let’s consider how Channing and her prospective equity partners could use a smart contract on a blockchain. There are a few exotic options that immediately come to mind (though by no means exhaustive), which Channing wants to write and sell. The first exotic she notifies prospective investors she’s willing to write is the following:

Example 1. Compound Options

Compound options are options on options. They are ‘compoundings’ of risky and therefore relatively inexpensive options within which are embedded one or more comparatively more expensive and ideally less risky options.

For instance, if investor R buys a call option on a call option on Channing’s goodserv, R has bought for the premium price of C1 the right to pay the first strike price K1 by the first exercise date T1, in order to receive a second call option C2, which then gives R the right to buy some referent asset A which Channing and R have agreed to ahead of time (and which is written into the terms of the contract) for the second strike price K2, by the exercise date T2. What is this reference asset? Maybe it’s the product or service Channing generates with R’s start-up funding. Maybe it’s a share of her goodserv’s value. Maybe it’s another call option. Maybe it’s a put option. Maybe its cash, which Channing’s goodserv will eventually generate. –But that’s the point: it can be literally whatever Channing and R agree to as the referent.

Why would Channing want to write and sell a compound option?

First off, Channing just needs some fast seed money to give her a chance to pay for her initial start-up costs. By writing and selling a call on a call to R (and other R’s), Channing acquires some immediate start-up funding, earned from the premium price of the option C1. If, after T0, Channing changes her business model, can’t get her act together, or suffers some set-back between T0 and T1, it’s likely R will not exercise the option for the premium price K1. On the one hand, Channing might be sorry to see R not exercise the C1 option by its expiration at T1, since this means she’ll now be lacking the subsequent second-stage funding she would have otherwise acquired, had R been willing to exercise this call option at the price of K1. But on the other hand, Channing owes nothing to R in return. She can walk away debt-free. She owes nothing to no one. She can try something else sometime in the future. However, if Channing makes good use of the funding she acquires by selling C1 to R; and if R sees this; it’s likely that R will either exercise C1 for the additional price of K1, which now gives R the C2 right to buy some reference asset A for some additional price they agreed to ahead; or R could also sell C1 before T1 to some other R, who will exercise C1 for the price of K1. Channing is probably ambivalent as to which of these occurs, since either way Channing is provided with additional start-up funding.

Why would R want to buy a compound option from Channing?

R has familiarized herself with Channing’s goodserv proof of concept, and either really likes its proposal, or at least believes it deserves a chance to succeed or fail on its own merits. But R doesn’t know what the future holds for Channing’s gooderv: it could be the next ‘big thing’, or it could prove unviable and fail. R does not want to lose too much money when taking a risk on Channing’s start-up, but R does want the option to invest in Channing’s start-up now, and possibly even invest more in the future. And after all, if Channing’s goodserv turns out to be successful, shouldn’t R be reasonably remunerated for believing-in and investing-in Channing’s start-up, when no one else would? By buying from Channing a relatively inexpensive call on a call for the premium price of C1 on her goodserv, on the one hand, R will not lose more than the initial premium price of C1, since if by T1 R is dissatisfied with the progress of Channing’s start-up, R simply lets the option expire unexercised, or possibly even tries to sell the option to someone else before T1 to try to recover as much of the C­1 money has possible. But on the other hand, when at T0, R pays the initial premium price C1, R is also acquiring the option to either exercise the option by T1 for K1, in order to now pay a new (and inevitably more expensive) premium price C2 to acquire the new (and more valuable) right to exercise the new call option C2 at T2 for K2; or once again, R could also sell her C1 option to someone else now for a profit, and simply walk away. If Channing’s goodserv begins to experience some success, or if R is otherwise satisfied with its progress, R is financially and/or psychologically remunerated for the early risk she’s taken. But if Channing’s start-up does not succeed, R has not lost very much money. R is not broke. R is not disillusioned. R can invest in something else sometime in the future.

In essence, then, a compound option allows both Channing and R to tailor their contract so as to mutually and equitably benefit from the success of this venture. It gives both of them some optionality. R is invested in Channing’s success. But R need not go broke wagering on Channing’s goodserv. Likewise, Channing is grateful for R’s early support, and is happy to try to reasonably remunerate R for wagering on the future success of her goodserv, when no one else would; but in no way is Channing’s prospective future interminably indebted to R.

However, compound options are only one method by which Channing writes and sells optionality to fund her start-up. She could also write forward start options, chooser options, or barrier options, and there are so many other exotic options as well. Let us briefly consider a few in closing.

Example 2. Forward Start Options

Forward start options are options that will start at some time in the future. The nature of Channing’s goodserv may be such that it will take some time to begin monetarily demonstrating its progress. By writing a forward start option, Channing can write and issue an option to fund the initial stages of her venture, without being compelled to immediately produce any nominal value. And R can hold this option without its value experiencing ‘time-decay’ (theta) as the date of its expiration nears.

Example 3. Chooser Options

Channing could also write a chooser options. After a specific period of time, the holder of a chooser option can ‘choose’ whether their option is a put or a call.

Example 4. Barrier Options

Channing may need to hire employees, in order for her goodserv to succeed. Channing could pay her prospective employees with barrier options. The payoff on barrier options depends on whether the referent reaches some pre-defined price point during a set period of time. This is a method of equitably-enfranchising those who may want to work with Channing towards the common success of her goodserv startup: if they do good work, they will be remunerated by the rise in value of their option; if they do not do good work, the value of their option will decline.

Channing can do all of this by easily downloading an application on her smartphone or computer, which allows her to advertise and customize the writing and selling of any of these four types of exotic options. A liquid market in exotics options will ultimately reduce transaction costs for both parties, and improve its market stability. But already from the beginning, if these exotics are executed by Dapps, written as smart contracts, and transacted on a blockchain, there is no reason for there to be anything but the most marginal of costs even from the outset.

But this is only one possibility. In a future post, SpecMat will examine how to englobe these Dapps within a DAO, by constructing a universal synthetic CDO.

For the Mammals we are….

[1]“Formalizing and Securing Relationships on Public Networks”, Nick Szabo, First Monday, No. 9 Sept. 1997

## Hey kids, do you like rhizomes?

Recent years have introduced profound evolutions in web technologies. Most significantly are new differentiations in blockchain technologies –namely, smart contracts, decentralized applications, and decentralized autonomous organizations.

Smart Contracts. Already in the early 1990s cryptographer and legal scholar Nick Szabo observed that combining digital protocols with user interfaces facilitated the creation of decentralized systems of contracts to hold, move, or divide-up any number of different classes of assets according to any rules pre-agreed to by its participants.[1] The problem, of course, was that no web technology actually then yet existed which were capable of addressing the complex of issues (e.g. the infamous “double-spending problem“, etc.) any attempts to implement an absolutely rhizomatic economy would convoke.

Enter the Blockchain. Then in 2009 Satoshi Nakamoto introduced the first fully-decentralized digital currency, known as the bitcoin, which enables peer-to-peer transactions wherever there’s internet access. Until recently, media attention has focused on issues such as its absence of a central issuer or backing by a national bank, its price volatility, and possible uses in criminal activities. In truth its radical innovation lies less with these issues, and even less with the bitcoin itself, than with the concept of the blockchain. Economic transactions in a blockchain consist of the digital transfer of money or some other unit of value for goodserv: these transactions are collected in ‘blocks’, and then ‘chained’ together, comprising a visible, verifiable, digital, decentralized public ledger. For this reason, any coupling of operators, however diffuse and heterogeneous, using a blockchain to organize themselves are immediately an autonomous, digitally-distributed, fully-decentralized consensus system, equipped with mechanisms for public memory, voting, and agreement on the order and character of all transactions –and importantly, therefore now with neither any need nor place for a centralizing authority. This, dear denizens of dromocracy, is a rhizome.

Bitcoin inaugurated the first wave of blockchain ledgers. What is now being called ‘the second-wave’ in blockchain technology underscores the realization that a blockchain can do much more than simply process coin-based transactions. In fact presently, what’s less clear are its limits. Even before the second wave, already in 2010, for example, Namecoin was applying Bitcoin’s consensus protocol to develop a decentralized name registration database, in which a first-to-file registrant wishing to start a goodserv (goods and services), e.g. “Channing’s Organic Greens”, or “Serra’s Eco-Architecture”, simply creates an account, which is timestamped on the blockchain ledger, and their start-up has now been publicly ‘named’ into existence.

Of course, this still begs the question of how Channing and Serra will fund their startup, without either already holding the necessary amount of cash, or else securing outside credit, which is to say going into debt, i.e. becoming a debtor, indebting themselves, their future work, and its future value in advance to some creditor? Can an independent goodserv startup be born without debt?

It can. Channing and Serra can do this. How? In short, through OTC writing and sale of exotic options (this is the topic of soon-to-come future post). Presently, of course, there is no venue for anyone -let alone Channing and Serra- to deploy this technology for purposes of starting a non-indebtified goodserv.

This is why I like Ethereum (Vitalik’s white paper is here) and their offshoots, e.g. Eris, etc.. Ethereum is currently the apex of second wave blockchain. It has developed a built-in Turing-complete programming language, equipping its users with a ready ability to create any variety of smart contracts. This means any two local operators can deliberate, agree-to, and create a short term contract to exchange goodserv or some financial asset for coin. And any larger set of operators can deliberate, agree-to, and create a long-term contract englobing the local operations. This amounts to now a fully-equipped operational capacity for a series of decentralized applications (Dapps) englobed within a DAO –a series of local and terminable smart contracts within a universalized and interminable, but always modifiable, decentralized autonomous organization. This means we now have the ability to actualize an absolutely rhizomatic economy, comprised of clusters of operators of exotic options, englobed within a universal synthetic CDO: in a word, dromocracy.

For this reason, over the course of the next several months, SpecMat will be examining blockchain and affiliated technological concepts, and ultimately collapsing them into our ongoing Dromocracy project.

[1] Nick Szabo, “Formalizing and Securing Relationships on Public Networks”, First Monday, Volume 2, No.9, September 1997, http://firstmonday.org/ojs/index.php/fm/article/view/548/469#introduction

## What Black-Scholes-Merton means to a speculative materialist

### Lesson Two

Even those persons paralyzed by anxiety over their lack of knowledge of financial economics will intuitively grasp that uncertainty pervades an attempt to ascertain what will have been the value of an asset in the future, relative to its subsequent past value now in the present. Can this even be done? BSM says it can.

Initially BSM announced itself as a risk-neutral, nonarbitrage model for pricing options. We will later expand on the importance that BSM isn’t quite used like this today. But let us presently observe that BSM is indeed a nonarbitrage model, albeit one whose condition of possibility and goal is arbitrage. However, BSM asserts that when deploying its partial differential equation to determine the value of an option, i.e. in order to know in the future what will have been the value of an option today, an operator must know four things:

(i) the option’s time to maturity (T)

(ii) the riskless interest rate (r)

(iii) the referent price (S0)

(iv) the volatility of referent price (σ)

The first three parameters are easily found. They’re either quoted in the market, or in the case of the first parameter, (T) time to maturity, i.e. the option’s expiration date, is written into the terms of the contract itself. However, the fourth parameter, volatility, is a bit trickier. BSM presumes a normal distribution, or ‘constant’ volatility –which amounts to erecting a thin epistemological wall to artificially insulate its model from jumps, irregularities, or volatile volatility, hoping those hideous animals on the other side won’t breach its perimeter, and stroll right in. Is to know volatility ontologically impossible? What even is volatility?

These queries have no quick redress, but are crucial for grasping the model of economy of deterministic chaos that is dromocracy proposed by D&G, and which in 2014 we have been and will be continuing to elaborate. Let us then move through its logic, or at least of it what we presently know.

If markets make a random walk, so too are plots of trajectories of the price movements of its assets, whose economic properties orbit along their markets’ surfaces. This means volatility is stochastic, unsteady, intractably irregular, a dark beast –and therefore this fourth parameter that an operator ‘must’ know to use BSM exhibits some determinism, yes, but a determinism wholly infused with chaos, or even is chaos.[1] Time spent studying the behavior of any class of financial asset causes quick realization that data on ‘past’ or ‘historical volatility’ (also called ‘actual volatility’)[2] is available but not dispositive for knowing future price movements. So any attempts by a BSM operator to divine ‘future volatility’ amounts to an attempt to solve a differential equation by way of a nondifferentiable function (*it can’t be done). Operators know this, and for this reason elect to retain BSM, but invert its equation to iterate ‘implied volatility’. Doing so, an operator must still know four things:

(i) the option’s time to maturity (T)

(ii) the riskless interest rate (r)

(iii) the referent price (S0)

(iv) the volatility of referent price (σ) (iv) the market price of the option

…but all four of which are now dictated or conveyed by the market, are messages transmitted in and by the market: the new fourth parameter is combined with the previous three parameters, and now used to derive the as-yet-unactualized volatility implied by the current market price of the option. The BSM operator, then, no longer plugs in the parameter of a normally-distributed volatility, which is to say a ‘constant’ volatility presumed to be actual, actualized, or ever actualizable, in order to derive the theoretical value of an option, but now plugs in the market price of the option to derive the theoretical value of volatility –i.e. the virtual value of volatility that an actual option price implies. Does this not render implied volatility a partial relic of the virtual that’s yet now paradoxically actual as well? In a future post we will take up this technological issue by opening up, to briefly peer inside, the peculiar material profundities interpellating implied volatility, which we believe is an intensive economic property: an odd, rare empirical instance of a differentiated aspect of the virtual that’s been refracted through itself and now dumped out into actuality; giving rise to ‘actual volatility’ at the same time such actualization of the latter covers or cancels it out.[3] Moreover, some attention directed to the robust Deleuzian-dynamical systems theoretic sense of the concept ‘intensive’ organically breeds our conviction that implied volatility is readily deployable as a fungible pricing mechanism, far more commensurate with the economic institutions and endemic behaviors of the denizens of a dromocracy, than that base and placid, one-dimensional, extensive medium of exchange we call ‘money’.

Presently, our brief tutorial on options will presume little background on our reader’s part.[4]

Financial derivatives comprise a class of financial assets. Options comprise a class of financial derivatives. In dromocracy, the exchange of options, especially exotic options (or simply ‘exotics’) comprise its principal class of exchange. Contingent local communities of becoming are ‘clusters’, rendering ‘clusters of exotic options’ (CEOs) one of its two economic institutions (the second being a universal synthetic CDO, to be outlined a bit later). In dromocracy, exotics among clusters are traded en masse.

The standard, if only sometimes correct definition of a financial derivative is an asset whose value derives from some other asset, often called a referent or underlier.[5] We’re supposed to tell you this; but it need not overly concern us, and at any rate, like the principles of Euclidean geometry, is not so much always wrong as it is only sometimes true. Our real concern is that an option is a nonlinear financial derivative producing a contingent claim; and that holding an option gives one the right to do something by a certain date, it gives the option holder choice, or optionality. Taleb tells us that ‘optionality is a broad term used by traders to describe a nonlinearity in the payoff of an instrument’[6], which will be particularly compelling to a reader who is now beginning to cognitively synthesize that rhizomes-nonlinearity-chaos-financial derivatives are the constitutive components of dromocracy, and that such novel model of economy is available to us if we so choose.

There are two kinds of options. There are ‘call options’, the holding of which gives one the right to acquire something at a certain price (called the ‘strike price’), on or by a future date (called ‘maturity’ or ‘expiration’). And there are ‘put options’, the holding of which gives one the right to part with something at a strike price on or by a future date. The terms ‘European’ and ‘American’ have nothing to do with where the options are written, read, or otherwise exchanged. Rather, European options can only be exercised on the day of their expiration, while American options can be exercised any time between their inception and expiration.

‘Operators’ are those persons exchanging options. Operators trade optionality. There are two types of operators: ‘writers’ and ‘readers’. To write optionality is to compose and sell an option for a fee to a reader, who now holds the right to choose to acquire some pre-agreed-to asset, whether an object or service, at a predetermined price, if mutually-pre-agreed-to conditions are met either at maturity or during the life of the option. To read optionality is to buy an option for a fee from a writer, who now accepts liability to deliver some pre-agreed-to asset, whether an object or service, at a predetermined price to the reader, if mutually pre-agreed-to conditions are met either at maturity or during the life of the option. Writers, then, issue optionality for a price, and accept liability if conditions written into the option are met. Readers accept optionality with a price, and exercise their choice if conditions written into the option are met.

What we have just said equally applies to exotics or vanillas, which are the two classes of options. Vanillas are standardized, and conventionally-structured. Exotics are bespoke, and have non-conventional structures. However, we will principally concern ourselves with exotics. It worth noting here, to begin, that pricing exotics can quickly become quite complicated in ways not conquerable by however-sophisticated modeling techniques, therefore generating available arbitrage opportunities for its operators. Importantly, this is due to exotics’ high-degree of nonlinearity: vanillas, yes, are already nonlinear, since all options are nonlinear assets; albeit exotics exhibit a higher degree of nonlinearity, as we will show. Exotics are to be the principal class of options exchanged in a dromocracy.[7]

BSM’s original assertion is that in theory it’s possible to construct a riskless portfolio, comprised of a position in options and some referent, such as stocks (though it could be any generic asset). We henceforth call this portfolio a ‘package’.[8]

Scholes says, ‘Black’s and my discovery was how to price options and to provide a way to manage risk.’[9] Derman and Taleb remind us this doesn’t mean that options are rendered riskless assets, or that an option’s actual price movements are in any way predictable, periodic, or nonstochastic.[10] Rather, the success of BSM’s pricing model pivots on hedging. And not just any hedging, but delta hedging –whose wager is that if an operator can get the delta of their package ‘right’, and then hedge accordingly and continuously, any price movements in an option position will always be offset by price movements in the referent position, and vice versa: and that these price movements offset one another means that the delta of the package at any given point in time, while not strictly zero, is nonetheless always striving towards it, tending towards it, asymptotically ever attempting to move yet closer to zero. The delta of the package is perpetually a becoming-zero.

[1] We’ll see that the issue is more involved than this. The initial model of price behavior used by BSM assumed that price changes are stochastic and normally distributed. To simply assert that a process is ‘stochastic’, or random, only further begs the question of the order and degree of its randomness –there are, after all qualitatively different classes of stochastization, so that any identification of a process as random must clarify to what class of randomness the process belongs (e.g. a Markov, Wiener, Itô, or Deleuzian process)? The answer given by BSM is that volatility exhibits a randomness that is normally-distributed, which makes it a Weiner process, but which turns out to be problematic. Today the standard financial economic definition of its class of stochastization is an Itô process, which we will show is also problematic.

[2] Our reader will be reminded that the three registers of reality in Deleuze’s ontology are actual-potential-virtual. ‘The actual’ is simply that which ‘is’ differentiated (what is sometimes mistakenly labeled ‘reality’). ‘The potential’ also is that which ‘is’, albeit only ‘is’ as a possibility (Deleuze identifies the potential as that which is subject to a probability distribution, but whose possible outcomes are therefore predetermined by the interlocutions of the actual and virtual). ‘The virtual’ is neither actual nor potential, and yet it exists ‘in reality’ nonetheless. A good deal of Deleuze’s project is to make technical recourse to mathematics and sciences to illustrate that while neither actual nor potential, the virtual comprises another register of reality altogether –a register structuring the space of what is possible to become actual.

[3] It is far from evident this notion is wholly comprehensible in Deleuze’s ontology. Its presentation, however, is far from a foreign element in his house. On the one hand, Deleuze toes the standard dynamical systems theoretic line that intensive properties often or always are canceled in those systems in which their spatiotemporal dynamisms generate the actualization of the extensive properties, whose very generation cancels them out. For example (‘There is an illusion tied to intensive quantities. This illusion, however, is not intensity itself, but rather the movement by which difference in intensity is cancelled. Nor is it apparently canceled. It is really canceled, but outside itself, in extensity and underneath quality.’) Difference & Repetition pg. 240; and (‘Intensity creates the extensities and qualities in which it is explicated….It is nevertheless true that intensity is explicated only in being cancelled in this differentiated system.’) Ibid pg. 255 Also see Ibid pg. 228. However, on the other hand, Deleuze’s (and D&G’s) special interest in complex, high-order, nonlinear chaotic systems (i.e. ‘systems of difference’) is their explication of relics of the virtual, e.g. intensive properties, whose logic can then be traced back up through the actual, and tinkered with. After all, why map, e.g. in phase space –if not to then tinker with matter’s evolutionary capacities? For example (‘it is in [systems of] difference that…phenomena flash their meaning like signs. The intense world of differences…is precisely the object of a superior empiricism. This empiricism teaches us strange “reason” [read: strange attractors], that of the multiple, chaos, and difference.’)

[4]The best book on options for the nonspecialist is John C. Hull Options, Futures, and Other Derivatives, Prentice-Hall 2009. For this reason, on our reader’s behalf we draw on Hull throughout Part IV.

[5] For example (‘A derivative can be defined as a financial instrument whose value depends on (or derives from) the values of other, more basic, underlying variables. Very often the variables underlying derivatives are the prices of traded assets. A stock option, for example, is a derivative whose value is dependent on the price of a stock. However, derivatives can be dependent on almost any variable, form the price of hogs to the amount of snow falling as a certain ski resort.’) Hull pg. 1; and (‘A derivative is a security whose price ultimately depends on that of another asset (called underlying). There are different categories of derivatives, ranging from something as simple as a future to something as complex as an exotic option, with all shades in between.’)Taleb pg. 9

[6] Ibid pg. 20

[7] In dromocracy there are two types of markets, ontologically-speaking, whose materiality is bound as one: there are commoditized products, which have standardized agreements in place to eliminate non-template inconveniences, and range from simple ‘spot-priced’ classic objects (e.g. things to eat and wear), to low-order forms of exotics (e.g. single barrier knock-outs); there are also nonstandard products, which are wholly exotic, and whose payoffs are specific to the instrument –these comprise the majority of contracts for work relations for the denizens of dromocracy. With such exotics, everyone is constantly tracking their Greeks. We thus agree with Taleb’s itemization of the basic difference between commoditized and nonstandard products, when he observes that ‘the real difference between [the two] is that one type is tailor made, with [higher risk and volatility, and] smaller traffic, while the other has features of a discount store with standard sizes and prices, but a higher volume.’ Taleb pg. 51

[8] Hull (2009) defines a conventional package (‘A package is a portfolio consisting of standard European calls, standard European puts, forward contracts, cash, and the underlying asset itself.’) pg. 555. We will ultimately wish to tailor this general concept to include an individual’s total portfolio of assets –generic and synthetic, comprised of exotic options and CLNs, as well as the synthetic assets whose total notional value comprises an individual’s universal synthetic portfolio, which is why we have neologized the term herein.

[9] Myron Scholes, “Derivatives in a Dynamic Environment”, The American Economic Review, Vol. 88, No.3, June 1988 pg. 351

[10] Emanuel Derman and Nassim Nicholas Taleb, “The Illusions of Dynamic Replication”, first draft Apr. 1995

## What the Greeks mean to a speculative materialist

### Lesson One

Let’s introduce the logic, then back up and unpack it.

Person: How does the package of the BSM operator chase delta-zero?

Speculative Materialist: By becoming delta-neutral, by always desiring to move yet faster towards zero.

P: But what about stochastization and nonlinearity? Won’t prices move, move randomly, and won’t volatility jump around?

SM: Well, yes, an operator needs to continuously recalibrate the delta of the package back towards its becoming-zero.

P: What’s recalibration? How does an operator continuously recalibrate?

SM: By dynamically replicating.

P: What’s dynamic replication? How does an operator dynamically replicate?

SM: With the Greeks: with delta (∆), gamma (Γ), vega (V), theta (Θ), and so on.

P: But what are the Greeks?

The Greeks

A standard financial economic definition of the Greeks is a map of the relation of the price of an option with respect to a variety of parameters;[1] by the term ‘relation’ we should understand ‘speed’, or ‘rate of change’. A speculative materialist’s brain often wishes to explode when ruminating on the ontological status of the Greeks. For us, they explicate the intensive differential relations between an option price and any number of parameters which would remain quite operative, but inaccessible to examination, strictly virtual, and thus unactualized were we lacking analytic recourse to their concepts.

We’ve conveyed our intention to tweak the Greeks, and before that to probe their peculiar ontological status for dromocratic purposes. However, let us first observe that risk has strong consequences for valuation and cash flow; but that risk is multidimensional, and dimension is not an economic invariant. In financial economics, each Greek letter (e.g. delta (Δ), gamma (Γ), theta (Θ), vega (V), etc.) purports to explicate a different dimension of risk –and its associated cash flow; so that an operator managing her Greeks will always be seeking to hedge her exposure to the multidimensional risks whose differential relations and amounts of relations perpetually supervene on her portfolio, affecting its actual value, and therefore it’s return.[2]

First, then, delta (Δ). Delta is first among Greeks, literally. It’s the first mathematical derivative of the product with respect to the referent, and the most important parameter to begin to understand dynamic replication by manner of continuous recalibration.[3] BSM’s first analytic virtue is to provide a formula for knowing delta.

Hull defines delta as ‘the rate of change of the option price with respect to the price of the underlying.’[4] Taleb defines delta as ‘the sensitivity of the option price to the change in the underlying price.’[5] More generally, this means that delta maps the speed of change between the option price and referent price. Like all Greeks, delta is an intensive economic property –which importantly, more generally means its concept denotes the speed of spread between valuations of the derivative expressed, represented, metricized, and territorialized as price, and valuations of its referent expressed, represented, metricized, territorialized as price. It is common to depict such expressions of delta in either a % or in total amounts. So for example, as Taleb explains, ‘a 50% delta is supposed to mean that the derivative is half as sensitive as the [referent] asset’ –this is delta in % terms; or ‘that one needs two dollars in face value of the derivative to replicate the behavior of one dollar of [referent] asset.’[6]

Standard industry definitions of delta will typically observe, as we have above, that it’s the first mathematical derivative of the product with respect to the referent asset. This means delta provides the primary numerics of the hedge ratio for any price moves between the referent and its derivative, when the two are combined to comprise some amount in a package. For this reason ‘delta’ and ‘hedging’ are terms which, while the former is somehow both more than but also only a subclass of the latter (for there is more than one way to hedge), are often combined so that ‘delta-hedging’, ‘hedging’, or ‘hedging with delta’ intends to denote that any infinitely small price moves in an option are offset by price moves in its referent, and vice versa.

And in a simple, linear, Euclidean world –which is to say in a world without drift, a world wherein the distribution of variations are normal –and not that there’s no volatility, but rather volatility is steady, oscillating, constant, its variations invariable, and thus globally predictable; in such a linear world, delta would obtain a value, that value would remain unchanged, and in turn would cause the efficient, effective, and sufficient achievement of a riskless package with delta-hedging: an operator would use BSM to tell her the number of units of stock (or other referent) relative to options she should hold to deterritorialize her package from a continual barrage of inundating, multidimensional risks; and constructing her riskless package by way of BSM would merely be a matter of static, linear, delta hedging, in a fixed, Euclidean, linear world.

At this time we remind our reader of D&G’s principle of asignifying rupture –one of six principles endemic to the rhizome model of economy outlined in Chapter 1. Asignifying rupture marks nonlinearity, nonlinearity has deep ontological-economic significance, and options are thoroughly nonlinear. The first good observation an options pricing manual will make is that options are nonlinear assets, and therefore the trajectories of an option’s constitutive parameters orbit amidst a nonlinear world. The second thing your manual will tell you is that this requires dynamic hedging, which in turn requires consideration of some second-order derivatives. We can and will be observing the epistemological significance of this deep ontological fact as well –albeit, as we will see, the issue obtains a qualitatively different profundity in dromocracy. For rather than seeking to mitigate, negotiate, or in some way tame nonlinearity for sedentary distributive purposes, the denizens of a dromocracy embrace its dynamics, urge its vortical propulsion, stoke its nomadic distributive thrust.

So we will demonstrate that dynamic delta-hedging consists of hedging on an ongoing and interminable, rather than static or one-time basis. There is neither true nor final ‘being’ to delta, but only ever its becoming. To dynamically-hedge with second-order derivatives is to continuously recalibrate, which renders the latter a financial economic method for interminably deterritorializing one’s package always back towards a zero that it will only ever asymptotically approach. Dynamic replication by method of continuous recalibration is then, for us, understood as a matter of interminable deterritorialization, a pure activity of intermittency isomorphic to the becoming that is the Cantor set –for it is infinitely-becoming zero, yet now comprises a substance unto itself. And insofar as dynamic replication requires second-order derivatives, such as for instance gamma, theta, vega, and rho; and that these Greeks lend us analytic purview into the multidimensionality of risk; this means that continuous recalibration provides us with a practical method for interminable deterritorialization, yes, but moreover is one whose technology provides for an operator, a set of operators, or indeed clusters of exotic operators to comingle with deterministic chaos, to drink from its open wealth –this is our interest in and wager on technology of continuous recalibration for the institutional and behavioral purposes of dromocracy.

[1] Taleb’s analysis of the Greeks are generally good (see Chapters 7-11), but his definition is characteristically careless. He invokes the term ‘sensitivity’ to denote the speed, or rate of change (‘“The Greeks”…denote the sensitivity of the option price with respect to several parameters’ pg. 10). Hull is less analytically-expansive, (see Chapter 17), but his definition is perhaps more robust (‘Each Greek letter measures a different dimension to risk in an option position and the aim of the trader is to manage the Greeks so that all the risks are acceptable.’ pg. 357)

[2] It should be observed that in any economy an operator is always virtually reading and writing their options to, among, and with others, and is therefore always faced with the actual problem of managing her multidimensional risk –the hedging of which may be easy or hard to come by, had cheaply or at great expense. Bob Meister has illustrated that the virtual exchange of options were already occurring between Adam Smith’s yeoman farmer and his financier (See his “Liquidity”, unpublished draft, Sept. 2013). The difference, for dromocracy, is that operators are actually buying and selling and swapping options, creating and destroying them, and all of their multidimensional and virtual but very real risks. In dromocracy, operators trade standardized options, yes, but significantly more so exotic and hyperexotic options as well. Moreover, because a war machine economy is equitable (but not equal), clusters provide operators a permanent set of impermanent venues for hedging their exposures to risk easily and cheaply. And because, as we will also see, by manner of universal synthetic CDO everyone is leveraged on top of everyone else –a leverage, natural and infinite– every operator is simultaneously an entire financial institution unto herself, together with her incessantly-changing cluster, and universally as an One.

[3] (‘A delta is expressed as the first mathematical derivative of the product with respect to the underlying asset. [This] means that it is the hedge ratio of the asset for an infinitely small move. Somehow, when the portfolio includes more than one option, with a combination of shorts and longs, delta and hedge ration start parting ways.’) Taleb pg. 115

[4] Hull pg. 360

[5] Taleb pg. 10

[6] Taleb pg. 115

## Economy of the War Machine Part IV. Chapter One (part a)

Yeah, so I don’t want to want to tell you what to do, but given where we’re going to be going, it might be good to briefly check in with the updated versions of this or this -but if not those, then at least look at this (if you want to -again, you do what you want to; I’m not telling you what to do, I’m telling you what you can do if you want to do it).

In A Thousand Plateaus D&G propose a new model of economy. No biggie. This project, the project of On Dromocracy (aka “Economy of the War Machine”) is, at our leisure, just kind of explaining what exactly this model involves. Here’s part a of Chapter One of Part IV of On Dromocracy.

Technological Issue. Interminable Deterritorialization

(Continuous Recalibration) (part a)

D&G draw our attention to the important technological issue concerning nomadic distribution. This is the issue of interminable deterritorialization. We believe the issue is best addressed through an exposition of the financial economic pricing method of continuous recalibration, because of the latter’s intimate ontological relation to dynamic hedging, or dynamic replication. That is to say, continuous recalibration proves a ready-made method for interminable deterritorialization –we need only be capable of, and willing to ‘tweak the Greeks’, i.e. to map, think through and on and with their concepts; to respect but probe and examine them, to tinker on their content, to see what more they can say; or as D&G say, to execute a little decalcomania.[1]

However, before one elects to ‘tweak’ anything whatsoever, some knowledge of the pre-tweaked version is nice to have. For this reason we should explain the Greek letters, first with a special focus on delta (∆), and later delta’s and the other Greeks’ relation to implied volatility, and in between that, the method for interminable deterritorialization that is the becoming delta-zero of continuous recalibration. This will serve us when examining our behavioral issue, wherein we itemize the intersecting desires of hedging-speculating-arbitraging –the simultaneous disposition of the denizens qua operators of a war machine economy, when dynamically arranging themselves into clusters of exotic options (CEOs), locally, and implementing a universal synthetic CDO (USCDO), globally.

Interminable Deterritorialization

Let us situate the technological issue of interminable deterritorialization in its proper textual and ontological context. Interminable deterritorialization is a class of deterritorialization, one whose issue abides in the more general question of how sedentary distribution and nomadic distribution ontologically differ in kind.

D&G note that an important element of the issue concerning nomadic distribution involves the question of ‘[what] is a principle and what is only [its] consequence’?[2] What do they mean? Obviously there’s no cause here for intellectual dogmatism on our part; no feigned sense of sobriety, nor obtuse commitments to some unyielding ideology, from whose departure we feel compelled to greet with derision. Those days are over, nothing could be less in the spirit of D&G. Rather, let us simply admit that nomadic distribution, like sedentary distribution, does concern itself with space (markets), it does concern itself with objects (assets) in space, it does concern itself with territories (property and property relations), with zones and regions, terrains and taxes. Yes, of course, nomadic distribution –like all distribution– concerns itself with what D&G call ‘points and paths’. Nomadic distribution, like sedentary distribution, ‘follows customary paths’; it too goes ‘from one point to another’, it is not ‘ignorant of points’.[3] Rather, D&G note that their differences pivot on the fact that in nomadic distribution, the points that determine the paths ‘are subordinated to the paths they determine’ –and that, importantly, ‘[this is] the reverse of what happens with the sedentary’: for in a nomadic mode of distribution ‘a point is reached only in order to be left behind; every point is a relay and exists only as a relay.’[4] So while it’s the case that every ‘path is always between two points’, in nomadic distribution the ‘in between’ of the paths takes up a consistency unto itself, ‘enjoys both an autonomy and a direction of its own.’ This is why D&G say that ‘the life of the nomad is the intermezzo’:[5] the nomad is always ‘in between’ that which is made, but this very in between now constitutes a substance in itself.

We will illustrate that this mode of distribution finds its commensurate pricing technology in the method of interminable deterritorialization that is continuous recalibration. It is also true that a becoming whose substance lies ‘in between’ two points will in practice demonstrate the abstract principle of the Cantor set we discussed in Part III. The Cantor set comprises an infinitely many dust of points, whose perpetual becoming produces a substance of space between its points –the principle of its activity is a continuous repetition of division, so that its set is continuously becoming zero, yet always remains embedded in a finite space, it is both infinitely numerous but infinitely sparse.

However, let us also pause to encourage our reader to not fail to observe that Chapter 12 opens these technically-grounded but otherwise creative ruminations with strict and sober definitions of two concrete problems. The first problem is institutional; the second is intellectual, or more perhaps appropriately thought of, in our opinion, as we noted, as behavioral. Their formal definition:

‘Problem I. Is there a way of warding off the formation of a State apparatus (or its equivalents in a group)?’ {the institutional problem}; and

‘Problem II. Is there a way to extricate thought from the State model’? {the behavioral problem}[6]

We should understand that D&G’s invocation of these problems amounts to a reminder, and that reminder is clear, returning us all the way back to Ch.1 of TP: D&G are recalling their prior commitment to saying “No” to both the arborescent (centralized) and fascicular (capitalist) modalities of the distribution of flows, and “Yes” and “How” to rhizomatic (war machine) flows.[7] Any hesitation by a reader of TP to understand the passages on nomadic distribution in this light, will fail to understand the proactive exercise required of us herein. For these are a prefatory set of problems outlined by D&G, for their readers, to whom they are appealing to help them think through and resolve. And only with these two problems defined and elaborated, and now opened up, can D&G then move deeper into Chapter 12’s dissertation on the materialism of nomadic distribution, whose general objective is to detail some related basic, affiliated problematics –and which again, as we have already argued, are principally technological, institutional, and then behavioral as well– when moving from ontology to economy, i.e. when moving from an exposition of the material wagers of nomadic distribution towards an economy of the war machine.

Moreover, at this textual point in Chapter 12, whereby D&G have just outlined these two problems, they now make sustained invocation to the notion of deterritorialization. Or rather, they make a special invocation to interminable deterritorialization –that rare mode of deterritorialization capable of immunizing itself from any counter- or reterritorialization; as if now providing their reader with a cue; as if appealing to, or pleading with us to help them think through as now a specifically economic problematic the issue concerning nomadic distribution, but now equipped with what we believe is best understood as the financial economic, practical-technological issue of interminable deterritorialization. Indeed, D&G are now enjoining their reader to search out, (re)engineer, or discover an instrument for its operation.

Optionality

Continuous recalibration is a practical method for interminable deterritorialization. To understand its prospective significance for dromocracy, our reader must understand the valuation model to which its technology originally attaches itself, namely, Black-Scholes-Merton (BSM).[8]

Even those readers paralyzed by anxiety about their lack of knowledge of financial economics will intuitively grasp that uncertainty pervades an attempt to ascertain what will have been the value of an asset in the future, relative to its subsequent past value now in the present. Can this even be done? BSM affirmed that it can. Initially BSM announced itself as a risk-neutral, nonarbitrage model for pricing options. We will later examine the importance that BSM isn’t quite used like this today. Let us presently note that BSM is indeed a nonarbitrage model, albeit one whose condition of possibility and goal is arbitrage. However, BSM asserts that when deploying its partial differential equation to determine the value of an option, i.e. to know in the future what will have been the value of an option today, an operator needs to know four things:

(i) the option’s time to maturity (T)

(ii) the riskless interest rate (r)

(iii) the referent price (S0)

(iv) the volatility of referent price (σ)

The first three parameters are easily found. They’re either quoted in the market, or in the case of the first parameter, i.e. time to maturity, which is the expiration date of the option, is embedded in the terms of the contract itself. The fourth parameter is a bit trickier. Is to know volatility perhaps even ontologically impossible?

If the market proceeds in a random walk, so too are plots of price movements of its assets. This means that volatility is stochastic, nonconstant, and therefore this fourth parameter an operator needs to know is deterministic but chaotic. One quickly realizes that any data on ‘past’ or ‘historical volatility’[9] is available but not dispositive for knowing future price movements. Any attempts by a BSM operator to divine ‘future volatility’ amounts to an attempt to solve a differential equation by way of a nondifferentiable function (*it can’t be done). For this reason, today operators retain BSM, but invert its equation to iterate implied volatility. We will end our consideration of our technological issue (to be presented in future posts) by opening up, to briefly peer inside, the peculiar but potentially profound material implications of implied volatility –which we believe is an intensive economic property giving rise to historical volatility, at the same time that actualization of the latter covers or cancels it out. Moreover, if we heed the full Deleuzian-dynamical systems theoretic sense of the term ‘intensive’, it produces some conviction that implied volatility is readily deployed as a fungible pricing mechanism, far more commensurate with the economic institutions and endemic behaviors of the denizens of a dromocracy, than is that placid, one-dimensional, extensive medium of exchange we call ‘money’.

We will introduce options without presuming much background on our reader’s part.[10]

Options comprise a class of financial derivatives, and financial derivatives comprise a class of financial assets. In dromocracy, the exchange of exotic options comprise the principal class of exchange. And communities, or clusters of exotic options (CEOs), are one of its two economic institutions.

The standard, if only sometimes correct definition of a financial derivative is an asset whose value derives from some other asset, often called a referent.[11] We’re supposed to tell you this; but it need not overly concern us, and at any rate is, like the principals of Euclidean geometry, not so much always wrong as only sometimes true. Rather our concern is that an option is a nonlinear financial derivative that produces a contingent claim; and that holding an option gives the option holder the right to do something by a certain date, it gives the option holder choice, or optionality. Taleb tells us that ‘optionality is a broad term used by traders to describe a nonlinearity in the payoff of an instrument’[12], which will be especially compelling to a reader who is now beginning to cognitively synthesize that rhizomes-nonlinearity-chaos-derivatives are the crucial constitutive components of dromocracy.

There are two kinds of options. There are call options, the holding of which gives one the right to acquire something at a certain price, known as the ‘strike price’, on or by a future date, known as ‘the maturity’ or ‘expiration’. And there are put options, the holding of which gives one the right to part with something at a strike price on or by a future date. The terms ‘European’ and ‘American’ have nothing to do with where the options are written, read, or otherwise exchanged. Rather, European options can only be exercised on the day of their expiration, while American options can be exercised any time between their inception and expiration.

In both finance and a dromocracy we call operators those persons exchanging options. Operators trade optionality. There are two types of operators: writers and readers. To write optionality is to sell an option for a fee to a reader, who now holds the right to choose to acquire some pre-agreed to asset, whether an object or service, at a predetermined price, if certain mutually-pre-agreed to conditions are met either at the end or during the life of the option. To read optionality is to buy an option for a fee from a writer, who now accepts the liability to deliver some pre-agreed to asset, whether an object or service, at a predetermined price to the reader, if certain mutually pre-agreed to conditions are met either at the end or during the life of the option. Writers, then, issue optionality for a price, and accept liability if conditions written in the option are met. Readers accept optionality with a price, and exercise their choice if conditions written in the option are met.

Lastly, there are two classes of options: vanillas and exotics. Vanillas are standardized options, and conventionally-structured. Exotics are bespoke options, and have non-conventional structures. It’s worth noting that pricing exotics can quickly become quite complicated in ways not conquerable by however-sophisticated modeling techniques, therefore generating available arbitrage opportunities for its operators. Exotics are the main classes of options exchanged in dromocracy.

BSM’s original assertion is that in theory it’s possible to construct a riskless portfolio, comprised of a position in options and some referent, such as stocks (though it could be any generic asset). For case-specific purposes, we will henceforth call this portfolio a ‘package’.[13]

Scholes says, ‘Black’s and my discovery was how to price options and to provide a way to manage risk.[14] Derman and Taleb remind us this doesn’t mean that options are rendered riskless assets, or that an option’s actual price movements are in any way predictable, periodic, or nonstochastic.[15] Rather, the success of BSM’s pricing model pivots on hedging. And not just any hedging, but delta hedging –whose wager is that any price movements in an option position are offset by price movements in a correlative stock position (or other referent), and vice versa: and that these price movements offset one another means that the delta of the package at any given point in time, while not strictly zero, is nonetheless always striving towards it, tending towards it, ever attempting to move yet closer to zero. The delta of the package is perpetually a becoming-zero.

Let us introduce this logic, then back up and unpack it:

How does the package chase delta-zero? By becoming delta-neutral. By always desiring to move yet faster towards zero.

But what about stochastization and nonlinearity? An operator is needed to continuously recalibrate the delta of the package back towards its becoming-zero.

What is this recalibration? How does an operator continuously recalibrate? With dynamic replication.

But what is dynamic replication? How does an operator dynamically replicate? With the Greeks: with delta (∆), gamma (Γ), vega (V), theta (Θ), and so on.

This is the logic. Let us unpack it.

In our next post we will first consider delta. It is the first among Greeks, literally. It’s the first mathematical derivative of the product with respect to the referent, and the most important parameter for understanding dynamic replication through continuous recalibration.[16] BSM provides a formula for knowing delta. Delta measures the ratio of change between the price of an option and the price of a stock. Thus, in a simple linear Euclidean world, i.e. a world without drift, in which volatility remains constant, and therefore a world wherein the value of delta remains invariant, achieving a riskless package by delta-hedging with BSM would be sufficient: an operator would use BSM to tell her the number of units of stock (or other referent) relative to options she must hold to deterritorialize her package from all risk. And constructing her riskless package by way of BSM would merely be a matter of static, linear, delta hedging, in a fixed, Euclidean, linear world.

Options, however, are thoroughly nonlinear. And assets in a nonlinear world require dynamic hedging, which means we will need to consider some second-order derivatives. To delta hedge is to hedge on an ongoing, rather than static or one-time, basis. To dynamically-hedge with second-order derivatives is to continuously recalibrate, a financial economic method for interminably deterritorializing one’s package always back towards a zero, which it will only ever asymptotically approach. To continuously recalibrate is to dynamically replicate. So dynamic replication by method of continuous recalibration –this is a matter of interminable deterritorialization, an activity of intermittency isomorphic to the becoming that is the Cantor set, for it is infinitely-becoming zero, yet now comprises a substance in itself.

That dynamic replication requires second-order derivatives, such as for instance gamma, theta, vega, and rho; that these Greeks lend us analytic purview into the multidimensionality of risk; and that continuous recalibration is understood to provide us with a method for interminable deterritorialization, yes, but moreover one whose technology allows for an operator or set of operators to comingle with deterministic chaos –this is our interest in continuous recalibration for the purposes of dromocracy.

In our next post, we will consider two simple examples, which we will cull and rework from Hull. These will serve to illustrate the basic dynamics of this technology, which we must first understand before understanding the ontological significance of implied volatility as a prospective pricing mechanism in a war machine economy, or more fully how continuous recalibration comprises a dynamic pricing method for its operators. Then, we can renter D&G’s wager on a rhizomatic model of economic flows, and see that continuous recalibration allows its operators, the denizens of dromocracy, to sit poised on the edge of nonlinearity, comingling with chaos, autonomous, healthy, viable, abiding in nomadic distribution.

[1] The standard financial economic concept of the “Greeks” (for examples, see Taleb (1996) pg. 10, and generally Ch.7-11; and Hull (2009) pg. 357, and generally Ch. 17) is often defined as a means of measuring the sensitivity of the price of an option with respect to a variety of parameters, but is better defined as the relationship between an option price and any number of parameters. Before we ‘tweak’ the Greeks, let us observe that risk is multidimensional, that dimension is not a geometric invariant; and so in financial economics each Greek letter (e.g. delta, gamma, theta, rho, etc.) purports to represent a different dimension of risk; so that an operator managing her Greeks will always be seeking to hedge her exposure to the multidimensional risks whose differential relations and amounts of relations perpetually supervene on her portfolio, affecting its value, and therefore it’s return.

[2] TP Ibid pg. 380

[3] Ibid pg. 380

[4] Ibid pg. 380

[5] Ibid pg. 380

[6] Ibid pg. 356, 374

[7] For example, recall the problem definition, original to Chapter 1: ‘The problem of the war machine…is [do we] need a general for n individuals to fire in unison? The solution without a General is to be found in an acentered multiplicity possessing a finite number of states with signals to indicate corresponding speeds.’ Ibid pg. 17

[8] Fischer Black and Myron Scholes, “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy, May/June (1997), and Robert C. Merton, “Theory of Rational Option Pricing”, Bell Journal of Economics and Management Sciences, 4 Spring (1973).

[9] ‘Historical volatility’ is also called ‘actual volatility’. Our reader will be reminded that the three registers of reality in Deleuze’s ontology are actual-potential-virtual.

[10]The best book on options for the nonspecialist is John C. Hull Options, Futures, and Other Derivatives, Prentice-Hall 2009. For this reason, on our reader’s behalf we draw on Hull throughout Part IV.

[11] (‘A derivative can be defined as a financial instrument whose value depends on (or derives from) the values of other, more basic, underlying variables. Very often the variables underlying derivatives are the prices of traded assets. A stock option, for example, is a derivative whose value is dependent on the price of a stock. However, derivatives can be dependent on almost any variable, form the price of hogs to the amount of snow falling as a certain ski resort.’) Hull pg. 1; and (‘A derivative is a security whose price ultimately depends on that of another asset (called underlying). There are different categories of derivatives, ranging from something as simple as a future to something as complex as an exotic option, with all shades in between.’)Taleb pg. 9

[12] Ibid pg. 20

[13] Hull (2009) defines a conventional package (‘A package is a portfolio consisting of standard European calls, standard European puts, forward contracts, cash, and the underlying asset itself.’) pg. 555. We will ultimately wish to tailor this general concept to include an individual’s total portfolio of assets –generic and synthetic, comprised of exotic options and CLNs, as well as the synthetic assets whose total notional value comprises an individual’s universal synthetic portfolio, which is why we have neologized the term herein.

[14] Myron Scholes, “Derivatives in a Dynamic Environment”, The American Economic Review, Vol. 88, No.3, June 1988 pg. 351

[15] Emanuel Derman and Nassim Nicholas Taleb, “The Illusions of Dynamic Replication”, first draft Apr. 1995

[16] (‘A delta is expressed as the first mathematical derivative of the product with respect to the underlying asset. [This] means that it is the hedge ratio of the asset for an infinitely small move. Somehow, when the portfolio includes more than one option, with a combination of shorts and longs, delta and hedge ration start parting ways.’) Taleb pg. 115

## Economy of the War Machine (Part IV. Overview)

Part IV of our Economy of the War Machine will arrive in several separate posts. Our outline is as follows.

Chapter One. Overview of Part IV. Elements of Nomadic Distribution

Chapter Two. A Technological Issue. Interminable Deterritorialization (Continuous Recalibration) (parts a and b)

Chapter Three. An Institutional Issue. Double Deterritorialization, or Numbering Number (Clusters of Exotic Options & a Universal Synthetic CDO) (parts a and b and c)

Chapter Four. A Behavioral Issue. Singularities, Attractors and Affects (Introduction  to a H20fall Economy) (parts a and b)

Overview of Part IV. Elements of Nomadic Distribution observed in Chapter Twelve

Abstracts of economic insight derived from dynamical systems theory (DST) have only hitherto been deployed in and by financial economics. But the latter’s approach is epistemological, exclusively an epistemology, a bad epistemology, and one whose method too often presumes a sedentary ontology, involving the sedentary use of nomadic technologies. By contrast, D&G enjoin us to probe the nomadic uses of nomadic technologies, to universalize the nomadic deployment of nomadic technologies, to become worthy of their event –to move them, with us, a we forward towards an economy of the war machine. In this way financial economics can become heterodox, a minor science, a speculative materialism. Can the bonds of debt be infinitely leveraged into and as universal equity? D&G’s deployment of DST affirms precisely this. We need merely unearth, seize, and commence to tinker-on the conceptual resources of DST built-into, if yet latent to, financial economics.

Let us agree that the whole viability of an economy of the war machine turns on the material capacities of nomadic distribution. All associative technologies, institutions, and ethics: if its material capacities prove inept, so too are these wagers.

Deleuze’s philosophical treatment of the general concept is well known. At some point in his major works, e.g. Logic of Sense, Difference & Repetition, one eventually encounters some devotion to its pure theoretic exposition. Perhaps it’s only natural, then, by which we mean born of habit, for our reader to herein expect us to confide that we must necessarily strive to clarify a streamlined economic application of nomadic distribution –as if it were obvious that our present task were to now peel some fat from meat, or separate chafe from wheat, in order to so to speak “lose” all of the “extra” (philosophical) weight, so that our more formal attire, the economic clothing of nomadic distribution, will better fit. However, let us not so quickly minimize the subtle but profound ontological assertion of DST –namely, of the univocity of being: that actually everything is diverse and multiple and different, but then again virtually the same. This means that much of what we would have previously regarded as either metaphorical or in need of discursive translation is in truth homologous and isomorphic, and hence in need of no tailoring whatsoever. Rather, we need merely overview those peculiar attributes marking the signature of the nomad, of nomadism, of nomadology, and can then subsequently move to immediately examine its purposive dynamics in the broadest-definition possible of an economic state space –and again, without any hint of implication that our case is made fully and finally herein (It is to perform the more comprehensive latter task that we are reserving Infinite Leverage (forthcoming, 2015)).

What, in Chapter 12, do D&G identify as the nomos of the nomadic? The shortest route to this answer is that nomadic distribution does not entail a parceling out of economic space, preproduced, fixed, enclosed, Euclidean, finite. It is not the redistribution of preproduced economic space, does not involve the assignation ‘[t]o each person a share’, and then proceed to regulate those shares. Rather nomadic distribution does precisely the opposite: it is the distribution of economic space itself, economic space produced as distributed in an open wealth (as opposed to redistributing preproduced wealth in a closed space). In this respect, nomadic distribution is indeed a mode of distribution –albeit, D&G remind us, ‘[i]t is a very special kind of distribution, one without division into shares, in a space without borders or enclosures.’[1] It is a mode of distribution that includes production itself.

An informed skeptic might grant that while in cosmology, biology, physics, and other fields studying complex systems we readily marvel at the nomadic distributive, alchemic, and indeed wholly unholy, unnatural, nonlinear capacities of Nature to produce space ex nihilo and ad infinitum, a likewise set of capacities, on which the economic wager of nomadic distribution is predicated, are not immediately apparent. But this is precisely what is at stake. The question is whether –when adjusting the aperture of DST to finance, economics, to financial economics, and when deploying its analytics for speculative materialist purposes– we can disclose, in order to effectively operationalize, the material capacities of nomadic distribution in and as an economy as well?

If we are then willing to grant that a set of operators will activate the affects endemic to those attractors through which an economy of the war machine functions; and if we concede that there must be some socio-political coordination to their dromocratic form –however fluid or mobile, heterogeneous and couth; we will allow that there are some crucial issues to address concerning nomadic distribution. These issues, we believe, are principally technological and institutional, but then behavioral as well. We are merely attempting to modestly push forward towards that rhizomatic mode of organization for the distribution of flows comprising a war machine economy, and are therefore self-assuming neither pressures of exhaustion nor systematicity. For this we will restrict ourselves to examining three basic prefatory issues.

These issues are:

(i) Issue One: A Technological Question.

First, there is the technological question of interminable deterritorialization. D&G’s earlier proposition of ordinal value immediately convokes the question of economic valuation in a smooth space, the latter of which is by its very definition understood to be wholly nonmetricized. And yet striations of value, its representation, and thus its metricization –whether going by “price” or some other name– must at some level differentiate itself to the denizens of a dromocracy. It may turn out that in a war machine economy, money, that contemporary medium of exchange by which valuations are metricized as price, and on which the classical symmetry between any given economic object and its image of value is achieved, is no longer needed (We recall Nietzsche’s passing assertion, made in a different but not wholly unrelated context, that our cause of rejection is no longer facts or proofs but now aesthetics and tastes): it may turn out that synthetic symmetry takes us to this point. We may end up rather preferring the numerics of implied volatility, by which to achieve a world of prices yet without money, and for this reason our elaboration of the technological issue will also take up its exposition. We have good reasons for understanding implied volatility as an intensive economic property; everything about the volatility smile causes this conviction. The unpaved path to arriving at the proper moment to open up this notion requires some consideration of the technological question, whose issue involves, as D&G point out, interminable deterritorialization –or what in options theory is known as continuous recalibration. However, to make this point, naturally, our reader must be prepared to learn about the class of financial derivatives called options.

(ii) Issue Two. An Institutional Question.

There is also the institutional issue, which D&G understand to be the double deterritorialization of Numbering Number. This could more colloquially obtain the label of the question of “social-economic institutions”, or of “economic-sociability”, or even “the political form of the economic” –if one insists on still deferring to various permutations of such historically-loaded terms. In truth our penchant is to regard this issue as mutatis mutandis a portion of the larger question of dromocratic community. Some readers may already know that D&G have highly novel ideas on this, which they pepper throughout TP, but then formally, densely, abstractly propose in terms of the autonomous arrangement of strange attractors that is the double deterritorialization of Numbering Number. In the course of our exposition of Numbering Number, we demonstrate that this institutional question was always a question about the economic institutionalization of topological and fractal forms. We’ve done some thinking ourselves on this, and are therefore prepared to provide our reader with a concrete introductory supplement to D&G’s passages on Numbering Number: simply, our assertion is that when conceived as a topological form, the double deterritorialization of Numbering Number is best actualized as, on the one hand, a global nonorientable economic surface, which is a universal synthetic CDO (USCDO); and on the other hand, a complex of local nonorientable economic surfaces, which are clusters of exotic options (CEOs). These dromocratic economic institutions, as we will show, are topological, in that they stretch and bend, fold over and twist. And yet their dimensions are nonrectifiable, discordant, intractably irregular, i.e. their dimension is not an integer, which means they’re fractals. Therefore, when conceived as a fractal form, the double deterritorialization that involves Numbering Number is best actualized as, again, on the one hand, a scaling cascade of tranched cash flows whose turbulent but periodic motions are organized around strange attractors (and their affects), which is achieved by a universal synthetic CDO (USCDO); and on the other hand, those clusters of exotic options (CEOs), whose stochastic motions are also organized around strange attractors (and their affects). In this way, we will show that USCDOs and CEOs are the proper institutional actualizations of what D&G theorize as Numbering Number, and as such, are the commensurate with the wagers of dromocracy –or what we call, when actualized, a H20fall economy.

(iii) Issue Three. A Behavioral Question.

Any notion involving attractors inevitably raises the issue of behavior, and raised by the issue of behavior is that of the issue of ethics. Our reader may well-know Deleuze’s take on Spinoza’s trope on ethics –that the question of ethics is always “of what are you capable?”– to which Deleuze’s reply was always that we have no absolutely idea of what our bodies, with matter, as assemblages, are capable. Less frequently explained, however, is the technical basis on which this assertion stands. For this reason, our third issue is an issue of the role and relation of phase singularities to the arrangement of attractors and their affects. Why? Because (a) a cascade of flows along attachment/detachment points endemic to structured tranches comprise a dynamic method for the fungible global arrangement of strange attractors –effected by a universal synthetic CDO; (b) the bespoke payoff functions of exotic options comprise a local but autonomous method for the fungible local arrangement of strange attractors –effected by small clusters of operators; these are called ‘clusters of exotics’, insofar as they’re neither fixed numbers (units) nor demarcated subspaces (communities), but rather mobile equity obligations whose infinite-length and infinitely-small volume comprises an economic substance; and (c) the institutional combination of (a) and (b) effects a critical stimulus for system phase resetting of attractors and their affects, i.e. a phase singularity, transitioning to modes of economic activity whose attractors (and their affects) previously lay in the flanks, but are now brought to the foreground. If we have no idea of what our economic institutions are capable, it is because presently they’re not. Let us recall that the principal question of dromocracy, inaugurated in Parts I and II, was how a fully-, or if not fully-, then an as-fully-as-possible-rhizomatic distribution of flows, and therefore neither segmented-centralized (arborescent) nor capitalist (fascicular), is realizable? How does a nonperiodic flow distribute itself when in fact that flow is free to distribute its own principals of distribution? This is the question for the rhizome model. But in truth it is also the question of chaos, to which DST has already provided a good reply. Moreover, our reader will see that this original question about the viability of the nonperiodicity of rhizomatic flows is reinvoked in Issue Three, as now foremost a behavioral question, whose effective redress pivots on the activity of arranging attractors. In D&G’s own words, it’s always a matter of bringing ‘a certain [attractor] in the flanks of the phylum…up to the surface by a given assemblage that selects, organizes, invents it, and through which all or part of the phylum [now] passes, at a given place at a given time.’[2]  As we will see, this wager on the formative power of attractors is that quilting point whose threads link Parts I and II’s introduction to the challenges facing an economy whose distribution of flows is rhizomatic, to Part III’s wager on ordinal value, and now Part IV’s prefatory examination of the financial economics of nomadic distribution.

Let us proceed on to our selected technological and institutional issues respectively, immediately below, in order to end our essay on dromocracy with the beginning of an address to this question, wherein we consider what we have called the behavioral issue as well.

[1] TP pg. 380

[2] TP pg. 407

[1] TP pg. 380

[2] TP pg. 407

## The Lure of, and Luring Shadow Banking

The post-2008 rise of shadow banking continues to generate a dustup between those who view its nebulous activity as a bulwark against both illiquidity and inefficiencies in the distribution of capital, versus those who hold it as a perennial threat to global stability. The most recent Economist includes a special report on shadow banking, in which declamations of the system’s potential to vitiate regulated, on-balance sheet activity is cast aside in favor of a more fecund discussion: the increasingly acknowledged potential for use as a viable form of risk securitization and lending.

Before one enters into discussion regarding the nebulous system, a proper definition is seemingly necessary. Shadow banking, however, is difficult to define, and for obvious semantic reasons (i.e. the signifier “shadow’). The following is taken from The Economist report:

“The definition of shadow banking is itself shadowy. The term was coined in 2007 by Paul McCulley, a senior executive at PIMCO, a big asset manager, to describe the legal structures used by big Western banks before the financial crisis to keep opaque and complicated securitised loans off their balance-sheets, but it is now generally used much more broadly. The Financial Stability Board, an international watchdog set up to guard against financial crises, defines shadow banking as ‘credit intermediation involving entities and activities outside the regular banking system’—in other words, lending by anything other than a bank […] Some of these competitors are simply banks by another name, trying to boost profits by cutting regulatory corners, which is a worry. But most are genuinely different creatures, able to absorb losses more easily than banks. They are a buttress rather than a threat to financial stability.”

Thus, shadow banking isn’t really just a system of recalcitrant competitors belying financial stability. Rather, as the report states, it has become a non-entrained system with all the plenum of traditional finance, now comprising a quarter of the global financial system, with assets reportedly reaching \$71 trillion in 2013 –signaling a growth of \$26 trillion in the last decade alone.

As I’ve argued before, it’s quite likely we can more readily account for the growth of shadow banking than the system itself, by beginning to think, or rather examine, its attractors as (Deleuzian) singularities. Why? Simply put, unlike the system itself, its basins of attraction are in fact not new at all. Just take, for instance, The Economist’s anecdote of Hall & Woodhouse, an English brewery founded in 1777. Until this year, H&W’s financial activity was a tableau of a “traditional” business that borrowed money in the form of bank loans, and then proceeded to gradually pay back the interest and principal, thus generating revenue, a steady income, a low level of debt, and a “pristine credit record”. Hall & Woodhouse, however, encountered some trouble in 2010 following the financial crisis, when their traditional lender, the Royal Bank of Scotland, informed the business it would only renew their line of credit for three years, instead of the usual five –and notably, now at a higher interest rate. Rather than conceding to this new, more expensive line of traditional credit, Hall & Woodhouse turned to shadow banking.

The Economist reports:

“They decided they needed more reliable long-term creditors, so they reduced their bank borrowing and turned instead to a shadow bank—a financial firm that is not regulated as a bank but performs many of the same functions (see article). The one they picked was M&G (the asset-management arm of Prudential, a big insurance firm), which offered them £20m over ten years.”

The Economist’s narrative here is that shadow banking offered H&W what traditional banks no longer could, or would, thus filling the void. However, this new trajectory, at least in Hall & Woodhouse’s case, is driven by much older, perennial business practices: securitization against risk via cost-effective loans. The attractors for businesses such as Hall & Woodhouse, then, haven’t changed. Shadow banking has been increasingly replacing traditional banks, which are now bogged down by post-crisis regulations and putative risk-minimizing measures. As The Economist puts it, “[t]his retreat of the banks has allowed the shadow banking system to fill the ensuing void.” But are we truly witnessing a meaningful exodus from tradition? The structure of shadow banking paradoxically mimes that of traditional lending, albeit in a more elliptical and unregulated dimension. So increasingly we see the discourse shifting away from oversimplified declamations against shadow banking, towards arguments that borrowers are drawn towards shadow banking because it offers what traditional banks can’t, as these banks are now “beset by heavier regulation, higher capital requirements, endless legal troubles and swingeing fines.” If we examine such activities in finance as Deleuze, and after him Manuel Delanda, conceive dynamical systems –namely, as comprised of trajectories whose basin of attraction are singularities, and wherein shocks or various critical stimuli help account for the creation of a bifurcated systems like shadow banking– this “draw” to the shadows, which accounts for the system’s subsequent growth, increasingly seems obvious.

Today regulators are apparently seeking ways to promulgate the upside of the shadow banking system, their intention being the attenuation of activities potentially leading to future crises, while simultaneously utilizing the system “for good”. Much of their focus, The Economist reports, is on leverage.

“One focus is leverage, the amount an institution has borrowed relative to the amount of loss-absorbing equity its owners have put into it. Most investment funds (with the notable but small exception of hedge funds) have minimal leverage or none at all, so if they run into trouble there is little risk that other lenders will suffer as a result. Alas, such contamination was a much bigger problem for the shadowy vehicles that issued asset-backed securities before the crisis.”

Much of the post-2008 discourse initially painted shadow banking as a principal contributor to the financial meltdown, partly due to the difficulty of evaluating off-balance sheet transactions, which proved so insidious, albeit only after the fact. That being said, we now better understand the cognitive response to post-crisis risk aversion (e.g., Hall & Woodhouse); consequently, we better understand the draw to shadow banking, and we better understand, to some extent, the risks associated with it. As The Economist report observes, “[t]he sooner the regime spells out which assets are protected, the sooner investors will take more care about risk. Shadow banking can make finance safer, but only if it is clear whose money is on the line.” So perhaps the important question here is a Deleuzian inquiry into the potential utilization of this new, bifurcated system of finance, which in turn will require that we move beyond traditional approaches to the topic, and now towards an understanding of the more fungible, even topological form of trading, lending, and securitization that is shadow banking. Indeed, shadow banking has already seemingly proved itself as a viable lending and borrowing tool par excellence in a post-crisis world, comprised of comparatively fewer, if any, nascent, state-violenced regulatory structures. Therefore, the question here is, how do we really wish to utilize such a system that holds the potential for disaster, but, conversely, the potential “for good” –and of course, as always, by what do we mean “good”? Mark Carney of the Financial Stability Board recently described shadow banking as the greatest danger to the world economy. The Economist report, however, is obviously more optimistic (The report celebrates shadow banking, while still betraying some anxiety: “Shadow banking certainly has the credentials to be a global bogeyman. It is huge, fast-growing in certain forms and little understood—a powerful tool for good but, if carelessly managed, potentially explosive.”)

We know shadow banking is inherently elliptical and difficult to map. But viewed through the analytical prism of the Deleuzian ontology, perhaps we will become more capable of mapping its growth, but subsequently must also be willing to then seek out concrete ways for its positive, alternative, even radical utilizations. Most of the discourse surrounding shadow banking articulates a deep and no doubt warranted concern over inadvertently instigating another liquidity crisis-turned-solvency crisis-turned-systemic-crisis. But is it enough for political economy to always concern itself with preempting a repeat of the same mistakes of the past? Is this to be our only vocation? Shadow Banking is indeed, in actuality, relatively new. So far as we seek to draw upon a metricized balance sheet to account for, understand, and regulate the correlative risks represented therein, there does seem to be a common, perhaps warranted, but at any rate apprehension that this system is too vague, nebulous, and potentially threating to system-stability. More proactive, however, may be to continue to prepare our imagination for our financial system’s alternative potential uses in ways that eschew habit and tradition (à laNietzsche). Only then can we thus elude the perpetual, surreptitious introjection of crippling anxiety over ongoing psychological, emotional, and cognitive attachments to traditional practices that vitiate our ability to actualize the virtual potential of finance, which is so necessary for rejecting the trope of insulating security against risk: for perhaps today our true task is to favor expanding universal risk against its perpetual threats by individuated insecurity.

— by Alex Montero

Cited web versions of The Economist report:

http://www.economist.com/news/special-report/21601621-banks-retreat-wake-financial-crisis-shadow-banks-are-taking-growing

http://www.economist.com/news/special-report/21601623-shadow-banks-are-easier-define-what-they-are-not-what-they-are-non-bank

## Economy of the War Machine (Part III of IV)

Part III. The Economic Concept of Ordinal Value in Chapter 9

Socially-necessary labor time, supply and demand, marginal utility, putative or nominal price, risk-weighted interest rates, or some combination of the above: what do all of these conceptions of the determinates of value share in common? In short, they are cardinal theories of value. And as such, according to D&G they are not so much completely wrong as they are both ordinary and partial and not general enough. Against a theory of cardinal value D&G advocate the concept of ordinal value, the latter of which always emanates between the flows of quanta, around singularities, and are only then metricized as segments and lines of, for instance, rates of return on labor or on capital, spreads between supply and demand, nominal and real interest rates, and so on. The economic indices of cardinal values differentiate from out of ordinal value, but then exogenously feed back into it, perpetually remaking the latter’s vacant interiority. This is the concept of ordinal value sketched by D&G in Chapter 9.

We said in Part I that our first concern is to familiarize ourselves with the complex of technical terms culled by D&G, then developed and deployed in the service of their project. Of course D&G’s project is neither exclusively nor first and foremost economic, nor political economic, as is ours herein –albeit as we have already begun to see, it is readily tailored to these concerns. Because D&G’s broad intention in TP is to inaugurate a new method of doing social science now definitively under the umbrella of conceptual resources endemic to dynamical systems theory, and insofar as political economy includes itself under the social scientific wager on the commensurability of its discourses, we can both exposit the concepts developed and deployed in Chapter 9 at the same time that we tailor our exposition of these technically-rigorous if highly-novel conceptual resources to our own task at hand.

Example (part I of II)

Let’s head straight away to the example used by D&G to illustrate the dynamics of ordinal value. Then we’ll back our way out to elaborate the concepts involved therein.

At this point in the text D&G have just asserted that ‘every society’, ‘every individual’ –and thus by implication and importantly for us every economy– are simultaneously ‘plied’ by two modes of segmentarity: ‘one molar, the other molecular’; and that there is a ‘double reciprocal dependency between them.’[1] The molar, which we will elaborate in depth below, is macroeconomic – rigid, veridical, Euclidean, arborescent. The molecular, which we will also elaborate in depth below, is microeconomic –fungible, horizontal, topological, rhizomatic.

D&G observe:

‘[T]he words “line” and “segment” should be reserved for molar organization, and other, more suitable words should be sought for molecular composition. And in fact, whenever we can identify a well-defined segmented line, we notice that it continues in another form, as a quantum flow. And in every instance we can locate a “power center” at the border between the two, defined not by an absolute exercise of power within its domain but by the relative adaptions and conversions it effects between the line and the flow.’

For example, D&G say:

‘Take a monetary flow with segments. These segments can be defined from several points of view, for example, from the viewpoint of a corporate budget (real wages, net profit, management salaries, interests on assets, reserves, investments, etc.).’

So this is D&G’s example, from which we derive their concept of ordinal value: their example here is ‘a monetary flow’ –cash flow, the flow of money, the distribution of money. And the ‘points of view’ from which one ‘defines’ its rigid segmentarities are, in other words and to begin with, the metrics recorded in any economic accounting report when attempting to account for, as in numerically-register or measure, a given value. These are the lines and segments, the stratified, striated metrics of the flow of money.[2]

However, they then clarify:

‘[T]his line of payment-money is linked to another aspect, namely, the flow of financing-money, which has not segments, but rather poles, singularities, and quanta (the poles of the flow are the creation of money and its destruction; the singularities are nominal liquid assets; the quanta are inflation, deflation, and stagflation, etc.). This has led some to speak of a “mutant convulsive, creative and circulatory flow” tied to desire and always subjacent to the solid line and its segments determining interest rates and supply and demand.’[3]

The poles and quanta and singularities –these comprise the mutant molecular dynamics of the flow of money, which as D&G put it ‘link’ the metricized flows of ‘payment-money’ to the more fungible, anexact, and topological flows of ‘financing-money’. And then this last line in the above quote is crucial: the molecular composition of the flow of money is ‘subjacent to’, viz. it underlies or lies just below the surface of the lines and segments that determine interest rates, generative tensions between supply and demand, and so on –the latter of which are, in other words, the extensive determinates of value, the value-form, or what D&G regard as cardinal value.

Molecular flows, then, are every bit as real as the metrics of the molar, it’s only that they are ‘subjacent’ to it. The molecular comprises ‘a mutant convulsive, creative and circulatory flow tied to desire and always subjacent to’ the molar determinates of cardinal value. It is strictly speaking not actual, but is every bit as real.

And so lastly:

‘When we talk about banking power, concentrated most notably in the central banks, it is indeed a question of the relative power to regulate “as much as” possible the communication, conversion, and coadaptation of the two parts of the circuit. That is why power centers are defined much more by what escapes them or by their impotence than by their zone of power. In short, the molecular, or microeconomics…is defined not by the smallness of its elements but by the nature of its “mass” –the quantum flow as opposed to the molar segmented line. The task of making the segments correspond to the quanta, of adjusting the segments to the quanta, implies hit-and-miss changes in rhythm and mode rather than any omnipotence; and something always escapes.’[4]

D&G’s understanding of banking power, or what is today more expansively referred to as finance, or what a political economist might dub the power of finance capital, is that it is ‘concentrated most notably in central banks’, but also in other places, such as ‘the World Bank…[and other] credit banks’ –their power ‘to regulate “as much as” possible the communication, conversion, and coadaptation of the two parts of the circuit’, i.e. the molar and molecular. It’s hardly a sovereign power, or what we typically think of as a ‘power center’; which is why, for instance, central banks yes do regulate, they ‘regulate “as much as possible”’ intercourse between the molar and molecular; but they are in truth ‘defined much more by what escapes them or by their impotence than by their zone of power.’ Power centers of the economy, such as central banks, attempt to mediate the molar and the molecular flows, but in reality, and as we so often hear, always “have the tiger (the mutant-molecular machine) by its tail (the molar machine)”.

Molar Machines, Molecular Machines

Obviously some elaboration is required. A first thing to observe is that since 1980, when D&G originally published TP, material developments in and of finance have caused changes to its discourse, which in turn have caused changes to its terminology. Therefore it will be prudent for us to update a few financial terms used in D&G’s example, to better specify both the contemporary relevance of their ordinal concept of value, as well as its possible application towards an economy of the war machine.

So as we said we would do, let us now back out our aperture from D&G’s example, in order to refocus our lens of analysis on the ontology developed in Chapter 9, whose conceptual deployment in their example we will reencounter once again –and whose terminology we will be updating at the same time.

The opening pages of Chapter 9 include a series of compelling observations about the ways in which social, political, economic phenomena are organized by modes of segmentation. As D&G put it, ‘[w]e are segmented all around and in every direction. The human being is a segmentary animal. Segmentarity is inherent to all the strata composing us.’[5] They proceed to outline three common modes of social segmentation –the binary (man-woman, adult child, etc.), the circular (the disks or coronas of house, neighborhood, city, state, etc.), and the linear (from family to school, from school to work, etc.).[6] To be clear, D&G do not here explicitly say anything by way of example about economic segmentation; but it is not the case that about it there is nothing to be said.

Although, as we have noted, planned economies are evident actualizations of the arborescent model of the distribution of flows, and the former are often represented as centralized through and through, D&G do not concede as meaningful any opposition between centralization and segmentation.[7] Rather, the principal differences in any manner of economic flows pivot on two different types of segmentarity –the rigid and the supple: as D&G note, ‘rigid segmentarity is always expressed by the Tree’ –it is macroeconomic, veridical and Euclidean; but there is also supple or fungible segmentarity, which is rhizomatic, and ‘results from multiplicities of n-dimensions’ –it is microeconomic, horizontal and topological.[8] These two different manners of flows are effected according to their different (abstract) machines: there is the (macroeconomic) machine of overcoding, which involves territorializations and reterritorializations of rigid segmentations; and there is the (microeconomic) machine of decoding, which involves deterritorializations of more fungible or supple segmentations.

There is still some conceptual unpacking for us to do here. However, let us be sure to proceed with caution. D&G have, to begin with, arranged an ostensible opposition between the molar and the molecular: in economic terms, this means that on the one hand, the molar is of the ‘realm of representations’, which in macroeconomic terms denotes (as they say) ‘large scale aggregates’, the rigid segments and lines, the metrics, the indexical determinates of cardinal value; and on the other hand, the molecular is a subrepresentational content that constantly leaks out of the molar, is irreducible to the molar, but then always crystallizes into and is only ever articulated, or capable of ‘representation’ in and by the molar. D&G define the molar as rigid, and the molecular as fungible. The molar is arborescent, while the molecular is rhizomatic. The molar is all metrics, but the molecular is nonmetrical. And on and on the elements of this ostensible binarity are delineated. However, this is precisely why we have said we must proceed here with caution. Like all ostensible binaries we encounter in the work of D&G, in truth this binary is not so much a binary, as we will see, but a differentiation –and as a differentiation any ostensible binary is only ever ostensible insofar as it’s a shred of a moment in the life of the differentiation, but one that’s quickly on its way to further fragmentation, further splitting, creating a new differentiation out of its prior differentiation. In short, it is a becoming.

This is certainly the case with the ostensible binary developed herein. First D&G have asserted that they do not regard as accurate or meaningful economistic distinctions made between the ostensible binary of centralization and segmentation –rather, that either segmentation already includes centralization as a subclass of itself, or (which is to say the same thing) that even centralization is always compelled to effect its own segmentations.[9] Then later, D&G will distinguish as ‘two kinds of segmentation’ the supple and the rigid, but then once again undercut the apparent binarity of this differentiation by asserting that not only is it not enough to oppose the centralized to the segmentary, ‘[n]or is it enough to oppose two kinds of segmentarity, one supple and primitive, the other modern and rigidified.’ For as D&G say, ‘[t]here is indeed a distinction between the two, but they are inseparable, they overlap, they are entangled’[10] (This is, properly speaking, both a re- and a de-differentiation –the supple and the rigid are ontologically distinct, but in actuality always entangled). The key thesis of Chapter 9 then follows (and our reader here will observe yet another, new ostensible binary-to-be-introduced-but-then-undercut-and-revealed-as-a-differentiation):

‘Every [economy], and every individual, are thus plied by both segmentarities simultaneously: one molar, the other molecular. If they are distinct, it is because they do not have the same terms or the same nature or even the same type of multiplicity. If they are inseparable, it is because they coexist and cross over into each other… [T]here is a double reciprocal dependency between them.’[11]

Given their immediate concern with social segmentation, D&G invoke as an example the case of an individual. They say: ‘Take aggregates of the perception or feeling type: their molar organization, their rigid segmentarity does not preclude the existence of an entire world of unconscious micropercepts, unconscious affects, fine segmentations that grasp or experience different things, are distributed and operate differently.’[12] And so too in economics, when it comes to the distribution of flows, ‘[t]here is a micro[economics] of perception, affection, conversation, and so forth. If we consider the great binary aggregates [of macroeconomics, e.g. goods and services, investment spending, consumption, savings, and so on] it is evident that they also cross over into molecular assemblages of a different nature, and that there is a double reciprocal dependency between them.’[13]

However, no sooner have D&G itemized this ostensible binary between the molar and the molecular, does it then reveal itself, retroactively, to have all along been a latent differentiation among three different kinds of lines –rigid lines, supple lines, and now several lines of flight. So now we see that (i) there are rigid lines: these denote the fixed and Euclidean binary, circular, and linear segmentations that characterize molar segmentations, the general and generalizing metrics, the codes and overcodings of macroeconomic representation (about which we will say more below). Then (ii) there are supple lines: these denote the ‘interlaced codes’ that still constitute segmentation, albeit now microeconomic segmentation –and while still segmented in and as binaries, circles, and linearities (the three common modes of segmentation), they’re marked by more fungibility or pliability, i.e. they are comparatively more plastic in their mode of composition (of the actual), which is only to say that while their mode of segmentation is more fungible, the outcome is always just as segmented: here it’s as if non-Euclidean motions are merely used to transform Euclidean objects into their images. So then what was once a simple ostensible binarity between the molar on the one hand, and the molecular on the other hand, has now split or differentiated into the molar on the one hand, which has three common modes of rigid segmentation (binary, circular, linear), and now two different modes of the molecular on the other hands, which on the new one hand has three supple modes of segmentation (binary, circular, linear), and on the new other hand has a dynamic set of lines, but which are immune to representation, as such. So on this new other hand, in addition to (ii), D&G now posit that (iii) there are also several lines of flight: while the rigid and the supple comprise two dissimilar modalities for the composition of lines and segmentations, two dissimilar manners of coding economic phenomena, and therefore comprise different modes of economic territorialization, by contrast the several lines of flight, as D&G put it, are ‘marked by quanta and defined by decoding and deterritorialization’ –and, it is absolutely important for us to note, as D&G wish underscore (by italicizing the text, as if now raising their voices to be heard): ‘there is always something like a war machine functioning along these lines.’[14] However, again, as they observe, the problem is –which in truth is an empirical problematic posed by the ontology of economics, and about which D&G are alerting us, enjoining their reader in Chapter 9 to think with them as a methodological challenge to overcome: ‘the three lines do not only coexist [in any given economic phenomena, or aggregate set of economic objects], but transform themselves into one another, cross-over into one another.’[15] Therefore, D&G now assert:

‘In view of this, it would be better to talk about simultaneous states of the abstract Machine. There is…an abstract machine of overcoding: it defines a rigid segmentarity, a macrosegmentarity, because it produces or rather reproduces segments, opposing them two by two, making all the centers resonate, and laying out a divisible, homogeneous space striated in all directions.’

The machine of overcoding is molar and macroeconomic, or rather actualizes as the representations of ‘economic macrosegmentarity’ –and as such, it is ‘linked’ to the State but is not precisely ‘equated’ with the State itself, insofar as the State is defined by D&G as merely the set of the assemblages that ‘effectuate’ the overcoding machine.[16]

But then at the ‘other pole’ of reality:

‘[T]here is an abstract machine of mutation, which operates by decoding and deterritorialization. It is what draws the lines of flight: it steers the quantum flows, assures the connection-creation of flows, and emits new quanta. It itself is in a state of flight, and erects war machines on its lines.’[17]

The machine of mutation is nonmetricized, nonmetricizing, and nonmetrical, it has no segmentations, no fixed Euclidean lines, no codes or coding capacities, and for all purpose is unactualized albeit very real. It is nomadic, not sedentary, it is topologically-distributive, but only ever representable in and as the molecularized segmented lines of microeconomics, or rather ‘economic microsegmentarity’.

What then is the relation between these two machines –in addition to the fact that they are often both simultaneously operative in the self-same phenomena? D&G note that the inter-physics of these machines is such that the ‘molar or rigid segments always seal, plug, block the lines of flight’, whereas the machine of mutation always produces its lines of flight ‘between the rigid segments and in another, submolecular direction.’ But that between these two poles, ‘there is also a whole realm of properly molecular negotiation, translation, and transduction in which at times molar lines are already undermined by fissures and cracks, and at other times lines of flight are already drawn toward black holes, flow connections are already replaced by limitative conjunctions, and quanta emissions are already converted into center-points.’ Moreover, and crucially for D&G, ‘[a]ll of this happens at the same time’:[18] in the economic sphere, lines of flight continually connect and unconnect, and then reconnect at some point sometime later; such lines of flight may ‘whip particle-signs out of black holes’, but then also ‘retreat into the swirl’ of their own self-made ‘micro-black holes or molecular conjunctions that interrupt them’; or they may effectuate a decoding, but then immediately ‘enter overcoded, concentrized, binarized, stable segments arrayed around a central black hole.’[19]

Ok, good. So the reader really does get a clear sense here of the fact that D&G are moving towards –and enjoining with us to think with them– a wholesale inauguration of a new heterodox method for doing economics, and now under the auspices of the conceptual resources endemic to dynamical systems theory. But the question that arises here is a question one will wish to ask of any self-proclaimed economic method: namely, given these aforementioned assertions, what are the causal determinates of –or if not determinates then at least relevant factors associated with– the abovementioned economic phenomena? For example, in the case of D&G’s economics, if the flows from the mutant molecular machine leak out of the cracks in the molar, but if the molar can in turn limit, block, or reterritorialize such flows; if lines of flight whip particle-signs out of nothingness, but then such particle-signs can dissipate and return to nothingness, endure recoding, effectuate another decoding, or even morph into further deterritorializations; in short, the question is: how or under what conditions does all this occur? Is it complete stochastization (which D&G have given us no reason to believe)? Or is it partially-deterministic and partially-stochastic (which D&G have also not said)? Or is it fully-deterministic (which, based on our understanding of dynamical systems theory, intuitively sounds wrong, and which D&G have also not given us reason to believe), and if so then of what brand of determinism (mechanical, efficient cause, formal cause, etc.)?

The short answer –which is Deleuze’s informed dynamical systems-theoretic reply to this question –issued ahead of time, first given in the opening chapter of his book on Bergsonism, then more fully in Difference and Repetition, and now in TP in abbreviated form– is that these are poorly-formulated questions, insofar as stochastization and determinism cohabit each other (this is already shown in Bénard cells, the most elementary exposition of a nonlinear system).

However, we must give our reader a more complete reply below. For this reason let us now revisit our consideration of D&G’s example, which will be followed by, in Part III, an exposition of (a) the dynamical systems theoretic conceptual resources deployed herein, followed by (b) D&G’s proposition of applying this ordinal concept of value for the purposes of an economy of the war machine.

Example (part II of II)

By now we well know there are qualitatively different modalities of economic flows. And we have observed that every economy is simultaneously ‘plied’ by two modes of segmentarity: ‘one molar, the other molecular’. We know that the molar is macroeconomic – rigid, veridical, Euclidean, arborescent. The molecular is microeconomic –fungible, horizontal, topological, rhizomatic. And that there is a ‘double reciprocal dependency between them’:[20] D&G observe that as a rule, the stronger the molar organization of an economy, the more it tends to reproduce ‘a molecularization of its own elements, relations, and elementary apparatuses.’[21] For as they say, ‘when the machine becomes planetary or cosmic, there is an increasing tendency for assemblages to miniaturize, to become micro-assemblages.’ And yet it’s also true that ‘molecular movements do not [only] complement but rather thwart and break through [the molar]: ‘it is as if a line of flight, perhaps only a trickle to begin with, leaked between the segments, escaping their centralization, eluding their totalization…. There is always something that flows or flees….’[22]

For this reason, D&G say:

‘[T]he words “line” and “segment” should be reserved for molar organization, and other, more suitable words should be sought for molecular composition. And in fact, whenever we can identify a well-defined segmented line, we notice that it continues in another form, as a quantum flow. And in every instance we can locate a “power center” at the border between the two, defined not by an absolute exercise of power within its domain but by the relative adaptions and conversions it effects between the line and the flow.’

For example, D&G say (and here we’re back to where we left off):

‘Take a monetary flow with segments. These segments can be defined from several points of view, for example, from the viewpoint of a corporate budget (real wages, net profit, management salaries, interests on assets, reserves, investments, etc.).’

We have already once considered, albeit in a more elementary manner, this example of ‘a monetary flow’ –as in cash flow, the flow of money, the distribution of money– which is the example D&G use to illustrate their concept of ordinal value. We have also already observed that the ‘points of view’ from which its lines and segments ‘can be defined’ are those metrics recorded in an economic accounting report, when the latter attempts to account for, as in numerically-register or measure, a given value; and that these are what D&G intend to denote when invoking the terms ‘lines’ and ‘segments’ –they are the stratified, striated metrics of the flow of money. So let us now more fully examine the contemporary relevance of this ‘point of view’.

One might have earlier asked, what exactly are D&G intending to denote when using this term “flow” in their example? What exactly is a flow? But this is precisely D&G’s point. For there are always two ways to answer this question: (i) The first is from the ‘point of view’ of its segments and lines, i.e. the determinative metrics of cardinal value: whether it’s the price of wages, net savings, net profits, rates of interest, capital and reserves requirements, investment spending, consumption, and so on; this approach is the common realist approach to representing value –cardinal value. It’s worth observing that while financial discourse and its terminology has altered somewhat since D&G first provided this example (in the 1980s), if we update its terminology we quickly see that and how this ‘point of view’ of a flow is vindicated. How so? Let us consider in more depth the overcoded flows represented by methods of economic accounting.

Economic accounting denotes a macroeconomic system of accounting whose reports record the segments and lines of the aggregate flow of money. The two most prevalent economic accounting methods in the United States are The National Income and Product Accounts (NIPAs) and the Flow of Funds Accounts. NIPAs are produced quarterly by the U.S. Commerce Department. They record the broadest macrosegmented economic data: all major macroeconomic metrics are represented –e.g. income flows, production of goods and services, investment spending, consumer spending, and above all and especially what is ostensibly the broadest metric of total market value of all goods and services produced within the geographical boundary of the United States, namely gross domestic product (GDP). What is total national cardinal value for any given quarter (and let us note here the term “quarter” is already both a temporally-segmented linearity (i.e. 1-2-3-4 quarters) and circularity (i.e. 4 quarters comprise 1 annual year))? –the answer is always found by looking to the line-itemized GDP, broken down into its various segments in NIPA: for example, personal consumption expenditures are segmented along the binarity of durable-nondurable goods; again, net exports of goods and services are also segmented along the binarity of imports-exports; government consumption expenditures and gross investment are segmented along the concentric circles of local-state-federal; and gross private domestic investment is segmented along a linear set of changes to fixed investment relative to changes in private inventories.[23]  NIPAs, however, while providing rigidly segmented data, otherwise unacccount for very few metrics on financial transactions, the latter of which are considerably more supple in their mode of segmentation. To correct this myopia, the Flow of Funds Accounts is published quarterly by the Federal Reserve. The Flow of Funds method of economic representation first segments the economy into a series of nonconcentric circles qua sectors: Households, Commercial Banks, Noncommercial Banks, Governments, Farm Businesses, Nonfarm Businesses, Monetary Authorities, other International transactors, and so on. Then a line-itemized balance sheet is constructed for each sector as a series of cardinal value binarities –for example, assets-liabilities (which represent current net worth), financial-nonfinancial assets, lenders-borrowers, funds raised through debt-equity, and so on. Each Flow of Funds statement also records linear changes to the distribution or flow of funds – for example, changes in holdings of financial assets and liabilities, changes in net worth, etc.[24]

For this reason economic accounting reports such as the NIPAs and Flow of Funds Accounts are considered indispensable sources for representing what D&G call ‘the well-defined segmented lines’ comprising the metricized distribution of monetary flows. However, limitations on the ability of this ‘point of view’ to capture those aspects of flows that do not lend themselves to such lines and segments are profound. We have already observed that NIPAs are widely-regarded as inept for failing to account for financial transactions, the latter of which always appear so contingent and fungible, but are also so determinative of the direction, amount, and velocity of monetary flows that NIPAs precisely seek to represent. The Flow of Funds Accounts attempts to correct this representational shortcoming, but in turn has its own limitations. For example, The Flow of Funds Account does not record intra-sectorial flows of funds, which means it fails to represent, or metricize, those differences in flows falling within –and therefore outside– its own segmentations. More importantly, it also does not capture any of the dynamics of intertemporal financial becomings: only those net flows occurring from one and to another discrete time period are represented by the metrics of the Flow of Funds Account, but never those changes occurring between two discrete time periods. And especially and above all, D&G emphasize that the overcoded molar organizations of monetary flows represented by economic accounting methods fail to grasp the quanta determinative of the microphysics of flows. For this reason, after D&G observe that:

‘a monetary flow with segments…can be defined from several points of view, for example, from the viewpoint of [economic accounting]’;

they then wager that one can also observe a flow distributing itself in ‘another form’ and at the same time. As D&G put it:

‘whenever we can identify a well-defined segmented line, we notice that it continues in another form, as a quantum flow.’[25]

What is this quantum flow, in their example?

‘[It is] the flow of financing-money, which has not segments, but rather poles, singularities, and quanta (the poles of the flow are the creation of money and its destruction; the singularities are nominal liquid assets; the quanta are inflation, deflation, and stagflation, etc.).’

The quantum flow is subjacent to the flow whose metrics are the elements of cardinal value. It is:

‘[a] “mutant convulsive, creative and circulatory flow” tied to desire and always subjacent to the solid line and its segments determining interest rates and supply and demand.’[26]

Simply put: the determinative metrics of cardinal value + this ‘mutant, convulsive, creative circulatory flow tied to desire and always subjacent’ to the former are, for D&G, what ordinal value is. And so if the answer to the question of “what exactly is a monetary flow?” for D&G has two answers; and if the first answer is (i) from the ‘point of view’ of economic accounting, the segments and lines of molar organization, which in turn represent the determinative metrics of cardinal value; then (ii) this other ‘point of view’ are the flows of what D&G (in the 1908s) label ‘financing-money’, but which we will today better understand to be the flows of finance, or financial flows. This aspect of monetary flows is neither indexed nor indexable by the metrics of economic accounting, it doesn’t effectuate itself in and through segments and lines, but rather always operates between poles, around singularities, and through quanta –and for this reason, D&G say, it is ‘tied to desire and always subjacent to’ the molar determinates of cardinal value. This second aspect of flow is difficult to represent, it resists metricization, and yet there it is.

To better understand the mutant molecular machine, whose lines of flight are generative of financial flows, let’s consider the meaning, relations, and meaning of the relations among its terms: financial flows, desire, singularities, poles and quanta.

Financial Flows. First, that D&G posit as the elements specific to financial flows poles, singularities, and quanta –this is to denote that poles are the creation and destruction of money involved in every act of exchange; singularities are nominal liquid assets, but which is probably more accurately today simply labeled ‘liquidity’ –i.e. the liquidity that is the requisite condition of possibility for every act of exchange (we will treat this notion below); and quanta are the becomings of inflation, deflation, disinflation, stagflation, and the like. Second, D&G assert that financial flows are all about belief and desire. Indeed, if financial flows comprise the ‘mutant’, ‘convulsive’ and ‘creative’ flows that are immune to any metricization by economic accounting, it is not so much because such flows are unquantifiable as that because such flows are irreducibly a matter of beliefs and desires, the methods used by economic accounting are therefore inept at capturing such dynamics. However, when D&G stress that from the ‘point of view’ of financial flows, the ‘two aspects of every assemblage’ are belief and desire,[27] they do not intend to imply an individuated content solely confined-in and the isolable-to the “heads” of economic actors. For as they note, ‘in the end, the difference is not between the social and individual…but between the molar realm of representations, individual or collective, and the molecular realm of beliefs and desires in which the distinction between the social and individual loses all meaning since flows are neither attributable to individuals, nor overcodable by collective signifiers.’[28] This fact is key to understanding the inherent analytical limitations of economic accounting –its mode of economic representation is perfectly capable of capturing the metrics of cardinal value. And yet cardinal values always arrive both too early and too late: they are too early because the deterritorializing creation, destruction, and transformation of beliefs and desires are precisely those lines of flight leaking out of macroeconomic indicators; and yet they’re also too late because the overcoding work of such macroeconomic indicators have always already reterritorialized any of their molecular movements. Indeed, this is why we observed in our Introduction, it is not so much that cardinal theories of value are completely wrong as that they are both ordinary (whereas we concern ourselves with the singular, or singularities) and partial (they’re only one half of the ‘double reciprocal dependency’), and therefore not general enough.

Desire. What then do D&G mean by belief and desire? If ‘a flow is always of belief and of desire’, and if the ‘mutant’ and ‘convulsive’ and ‘creative’ flows of finance are always ‘tied to desire’, we are already here in Chapter 9 receiving a first cue from D&G about how to move towards an economy of the war machine. First, on belief: D&G do not provide their own definition of belief, so we will assume its common definition –namely, the affective state that a conjecture or premise is true. And on desire: D&G’s assertion on desire is worth quoting here in full, insofar as their wager on economic importance of desire is later deployed in the service of their practical outline for such an economy, elaborated in Chapter 12. They say:

‘Desire is never separable from complex assemblages that necessarily tie into molecular levels, from microformations already shaping postures, attitudes, perceptions, expectations, semiotic systems, etc. Desire is never an undifferentiated instinctual energy, but itself results from highly developed, engineered setup rich in interactions: a whole supple segmentarity that processes molecular energies and potentially gives desire [its] determination.’[29]

We know that there is no such thing as a belief in itself –belief is always a belief in or of something. So too for D&G desire has no in itself. There is never an articulation or expression of ‘pure’ desire, no such pure desire exists. Rather, desire is always a desire ‘for’ or ‘of’, and the ‘for’ or ‘of’ of desire is always inseparable from a complex of complex assemblages, it is only ever differentiated through a ‘highly developed, engineered setup’ of assemblages that ‘necessarily tie into molecular levels, from microformations already shaping postures, attitudes, perceptions, expectations, semiotic systems, etc.’

Singularities. If beliefs and desires are ‘inseparable’ from assemblages, what do D&G mean by assemblages? How do assemblages ‘engineer’ the amount, direction, and velocity of beliefs and desires? Any reference by D&G to assemblages should always be understood in terms of singularities, for an assemblage at its most basic is for D&G simply a ‘constellation of singularities.’[30] The concept of singularity has a robust mathematico-scientific denotation, and its use by D&G should be understood in this light: singularities are concrete universals, and along with affects (viz. morphogenetic properties) are the constitutive elements of any multiplicity. Singularities are those motionless, empty, atemporal organizing centers, those arrhythmic vacant points around which the spatial patterns of timing in a complex system, such as for instance an economy, will coordinate. Singularities are, in short, what the biologist and great dynamical systems theorist Arthur Winfree has called ‘the special point upon which the whole mystery turns.’[31] For this reason, and for us in our consideration of Chapter 12 (in Part IV), understanding the powerful method for arranging singularities that is the tranching process of structured finance is a matter of understanding the special point upon which the whole mystery of how to effect an economy of the war machine turns. That liquidity is a singularity –or what D&G in the 1980s label ‘nominal liquid assets’, but which we have updated as simply ‘liquidity’, the liquidity that is the requisite condition of possibility for every act of exchange– is both a compelling notion and yet also a mystery indeed. For any serious student of finance well knows that liquidity often appears to be a mere property of an asset: we call this ‘transaction liquidity’, and understand that an asset ‘has’ liquidity if it is readily exchanged for its image of value as money (the object has liquidity, it is a property attached to the asset). But liquidity can also appear to infuse or characterize those markets that different varieties of assets will populate: here one is now no longer speaking of an asset’s liquidity, but now of ‘market liquidity’, and will then attribute ‘liquidity’ to a space of an exchange if its participants can unwind their positions quickly without excessive price deteriorations to the assets involved (note the subtle but important ontological shift from liquidity as purely an objectival property to now property of space with objectival consequences). But of course liquidity today can also just as readily denote a property ostensibly attaching itself to a borrower, what is today labeled ‘funding liquidity’: this involves a borrower’s creditworthiness, and especially his or her or its ability to continuously finance assets at an acceptable borrowing rate, so as not to experience the conversion of illiquidity into insolvency (once again note the subtle but important ontological shift from liquidity, again not an objectival property, and now not as a property of space with objectival consequences, but as a property of a subject with objectival and spatial consequences). How then should one understand the mysterious thing called liquidity, in that it is said to adhere to an asset, market, or borrower alike –as if it were circulating around and between them, but in truth never settling finally into one or the other? D&G are replying here that if liquidity proves to be a mystery, it is also the special point upon which the whole mystery turns; it is a motionless, always vacant, organizing center around which the affects endemic to an exchange are always coordinated, and from which the elements of cardinal value are refracted out into the actual; and yet –as we will see in Part IV– it is these same elements of the cardinal that then feed back into liquidity, remaking, resituating, reshuffling it anew.

Poles and Quanta. Poles are the creation and destruction of money involved in every act of exchange. Why? If we simply define an exchange as the transformation of an economic object into its image of value as money, we quickly see why D&G invoke the concept of poles: on the one side of a bilateral transaction lies the liquidation of the asset for money, on the other side lies the asset purchased with liquidity, or money, which is to say that the calcification of a given amount of liquidity is the price that’s paid for an asset. Every act of exchange therefore occurs between two poles: and the poles situate this dual-tiered simultaneous event between a positive charge (+), which is the creation of money, and the negative charge (-), which is the destruction of money. Quanta then: quanta are instantiations of inflation, deflation, disinflation, stagflation, and the like, and which operate along the poles, but only ever effectuate themselves within the relations between an asset and its image of value as money. Economic objects never “have” inflation, deflation, and so on, as if the latter were properties of an object; rather it’s the relations, the spreads between different objects and their images of value as money that experience or obtain inflation, deflation, etc. Quanta are not objects, then, but the stochastic processes around which and through which objects obtain their objectivity. In this respect, inflation, etc. is like weather –it is a haeccity, a stochastization of movements that only articulate themselves in objects, without yet ever being reducible to such objects.

To summarize, then, we can say that quanta and flow are the stochastic processes whose dynamics take shape or coordinate around singularities, and which then refract out into lines and segments, i.e. the metrics of representation –the representations of cardinal value. Hence the thesis of ordinal value is: monetary flows emanate from the double reciprocal determination of the mutant molecular and molar machines, they each have their different ontological modalities, and they each comprise two dissimilar systems of reference, albeit they are two circuits of flows that are materially-interconnected and always flow as one. But –and this is D&G’s ‘but’ to be developed in Chapter 12, and given their concept of ordinal value outlined in Chapter 9– if an operator or sets of operators were to attempt to enter into or rather between these ontologically distinct but actually conflated circuits, it must be through the molecular. This is the ontological importance of the concept of ordinal value. We illustrate its political wager in Part IV.

[1] Ibid pg. 213 {my emphasis}

[2] We will elaborate this point in more depth below (in Example (part II of II)). For now let us observe that “economic accounting” is the contemporary financial term (which, incidentally, was not commonly used term when D&G wrote TP) to denote the record keeping system of transactions of the principal segments (called “sectors”) of the economy. Such records report macroeconomic and financial flows data.

[3] Ibid pg. 213 {my emphasis}

[4] TP pg. 217

[5] Ibid pg. 2018

[6] It is relevant to notify our reader that the three principal Euclidean geometric motions –which are rigid motions, called congruent motions– are reflection (of binary images), rotation (in circles), and translation (which is linear). Segmentations and lines are the rigid motions for organizing the distribution of social flows.

[7] ‘There is no opposition between the central and the segmentary. The modern [economic] system is a global whole, unified and unifying, but is so because it implies a constellation of juxtaposed, imbricated, ordered subsystems; the analysis of decision making brings to light all kinds of compartmentalizations and partial processes that interconnect, but not without gaps and displacements’ For this reason, ‘the classical opposition between segmentarity and centralization hardly seems relevant. Not only does the State exercise power over the segments it sustains or permits to survive, but it possesses and imposes its own segmentarities.’ Ibid pg. 210, 209-210

[8] Ibid pg. 212

[9] Ibid pg. 224

[10] Ibid pg. 213

[11] Ibid pg. 213

[12] Ibid pg. 213

[13] Ibid pg. 213

[14] Ibid pg. 222

[15] Ibid pg. 223

[16] Ibid pg. 223

[17] Ibid pg. 223

[18] Ibid pg. 223-224

[19] Ibid pg. 224

[20] Ibid pg. 213 {my emphasis}

[21] Ibid pg. 215

[22] Ibid pg. 216

[23] Peter Rose and Milton Marquis, Money and Capital Markets: Financial Institutions and Instruments in a Global Marketplace, Peter Rose and Milton Marquis, McGraw-Hill Irwin, 2008 pg. 80

[24] Ibid pg. 83

[25] TP pg. 217

[26] Ibid pg. 213 {my emphasis}

[27] Ibid pg. 219 D&G in actuality are using Gabriel Tarde’s work to tease out this position, but textual content and context render it easy to attribute this notion to D&G.

[28] Ibid pg. 219

[29] Ibid pg. 215

[30] Ibid. pg. 406

[31] Arthur Winfree, When Time Breaks Down: The Three Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias, Princeton, 1987 pg. 12

## Economy of the War Machine (part II of IV)

Part II. Three Models of Economy in Chapter 1

There are, according to D&G, as outlined in Chapter 1, three conceptually-distinct but ontologically-interwoven models for the composition of the assemblage of an object. For our purposes, we have said we will take up the object qua assemblage that is the set of properties and their relations we call “the economy”. To be clear, it is not that D&G think that any given economic system is fixed, finally-committed to, or structurally-overdetermined by any one of these models. Rather, economies constantly combine and recombine such modalities in a fluid, fungible process of becoming, a becoming of flows, even if it is the case that in actuality one such model usually tends to overcode the other two in their functional capacities.

The first type of economy is the root-economy, or often more appropriately-labeled by D&G as the arborescent model.

1. The second type is the radicle or fascicular model of economy.
2. The third type is the rhizome model. As the essays of TP proceed, D&G also begin using the term ‘economy of the war machine’[1], or ‘dromocracy’: the terms our synonymous; we will demonstrate this is best actualized as a H2Ofall economy.

Let us consider each model.

Arborescent Model

‘The first type of [economy] is the root [economy]….The tree and root inspire a sad image of thought that is forever imitating the multiple on the basis of a centered or segmented higher unity. If we consider the set, the branches-roots, the trunk plays the role of opposed segment for one of the subsets running from bottom to top: this kind of segment is a “link dipole”, in contrast to the “unit dipoles” formed by spoke radiating from a single center.’[2]

D&G enjoin us to think of the manner by which trees distribute their flows. This occurs by way of linear, unidirectional processes. A centralized trunk splits-in-two, and such binaries perform a dualist distribution of flows. Trees, of course, are not always strictly veridical in their distributional organization, but for D&G that is quite beside the point, insofar as they’re concerned with the images of flows articulated by each model. Rather, they’re simply using a tree trope to define any veridically-organized economic system as an assemblage that proceeds in the manner of the arborescent model.

From ‘centers of power’[3] the spokes of an arborescent economy radiate outward as a unified, synchronized set of homogenized processes. Their affects link various ‘unit dipoles’ –institutions, actors, assets, and so on– which incrementally extend, or expand, in a linear direction, always following pre-circumscribed, fixed, Euclidean, established routes. As D&G put it: ‘Arborescent systems are hierarchical systems with centers of significance and subjectification, central automata like organized memories. In the corresponding models, an element only receives information from a higher unit, and only receives a subjective affection along preestablished paths.’[4]

In an arborescent model the object is whole, the object is total and totalizing. For this reason, we quickly recognize that the arborescent model of flows characterizes so-called “planned economies”, whereby determinations over the distribution of capital, cash, and monetary flows are hierarchically-arranged ‘on the basis of a centered or segmented unity’.[5] The leather-cap communist, or tobacco-pipe socialist manner of the distribution of flows, whose topic is the retroactive critique of Spufford’s Red Plenty, the disdain of Hayek’s most spirited work, and Lenin’s advocations in The State and Revolution, for example, most-closely embodies the arborescent model. But let us not overlook the presence of elements of such veridical determinations by, among other institutions, central banks in today’s bubble-gum capitalist economies. This may be less obvious to our reader. For this reason some discussion of it is warranted.

‘Because wages and prices do not adjust quickly enough to keep the economy at full employment all the time, sometimes monetary and fiscal policies are needed…’

— former Chairman of the Federal Reserve, Ben Bernanke[6]

‘Imagine the trading floor in a movie about Wall Street, except that the people at the desks look like graduate students, dress business casual, and work in library like silence. There are few seminar-size rooms off the main floor. In one, on the spring morning I visited, there were five very serious looking people. They were buying, in daily quantities small enough for financial markets to digest, long-term U.S. government bonds amounting to thirty billion dollars every month. In the next room, were seven people buying mortgage-backed securities (twenty-five billion dollars every month). Can a spectacle so lacking in the indicia of importance –no pageantry, no emotions, not even speaking –really be the beating heart of capitalism?’[7]

— reporter, Nicholas Lehman, describing his experience ‘watching’ the practice of quantitative easing by the Federal Reserve

The Federal Reserve combines ‘open market operations’ (somewhat ironically-labeled) with a sovereign decision on short term interests rates, to effect a root- or tree-like mode of distribution of flows. Such central bank action effectuates the amount and velocity of money in the economy, therefore imbues an amount and sets a price for liquidity in financial markets, and subsequently determinatively influences a range of prices of cash commodities. When the Federal Open Market Committee (FOMC) convenes every five or so weeks, it’s meetings are premised on an understanding that it’s task is to act as a ‘center of significance and subjectification’: it is both legally-authorized and legally-charged with the task of acting as a ‘link-dipole’ between money and capital markets, on the one hand, and the rest of the ‘unit-dipoles’ of the economy (e.g. commodities markets, equities markets, consumer goods markets), on the other. This is to say that the central bank plans and implements a target-interest rate, it outright controls the money supply (through the sale and purchase of Treasuries), and therein continually issues ‘messages’ to the market by way of the hierarchical distribution of information (significance) and veridical determination of the term-yield structure (subjectification).

To observe that the Federal Reserve’s dual mandate is to act as a ‘central automata like organized memories’ is not hyperbole, but merely a fancy way of observing that it enacts its role as an institutionalized memory for the spokes of the economy by controlling the benchmark rate for the price of money; and so each ‘element’ of information that then congeals in the price of an asset has always first received information from this ‘higher unit’. The prices of assets in financial markets therefore only ever “randomly walk”, and the interlinked ‘unit-dipole’ markets only ever comprise an “efficient market”, when this is the case, because the first moment of the randomly-walking efficient market is its receipt of ‘a subjective affection along preestablished paths’: e.g. from the Fed’s FOMC activity and then FOMC notes to the Bloomberg terminal; from the Bloomberg terminal to the news agencies and (high-frequency) traders and other market makers; and from there throughout the rest of the so-called efficient market, the prices of all assets are then free to randomly walk.

Fascicular Model

‘The radicle-system, or fascicular root, is the second figure of the [economy], to which our modernity pays willing allegiance….This time natural reality is what aborts the principle root, but the root’s unity subsists, as past or as yet to come. We must ask if reflexive, spiritual reality does not compensate for this state of things by demanding an even more comprehensive secret unity, or more extensive totality….This is to say that the fascicular system does not really break with dualism…[for] unity is consistently thwarted in the object, while a new type of unity triumphs in the subject.’[8]

D&G assert that arborescent economies testify to both an ‘oldest’ and ‘weariest kind of thought’. This, perhaps, already points us towards why the most earnest attempts to fully-effect centralized planned economies always turn so conservative so very quickly, and why they were doomed from the outset. And yet this also reveals why ‘link dipoles’ such as the Federal Reserve, cannot be wholly-identified with an economic assemblage whose model is mutatis mutandis arborescent. Elaborating the arborescent model, D&G deride those beliefs that ‘the [economy] imitates the world, as art imitates nature’, as if we were able to recreate ‘procedures specific to it that accomplish what nature cannot or can no longer do.’ Or again, the idea that ‘[t]he law of the [economy] is the law of reflection, the One that becomes two’ –D&G warn that ‘whenever we encounter this formula, even stated strategically by Mao or understood in the most “dialectical” way possible, what we have before us is the most classical and well reflected, oldest, and weariest kind of thought. Nature doesn’t work that way…’[9]

However, D&G also note that even when one believes to have achieved a kind of natural multiplicity, this too may turn out to be false; that one often acquires the pretense to adventitious multiples, but which conceal an even more totalizing unity belying it. They assert that this is the case with the radicle or fascicular model of economy. As we alluded to above, actualizations of its model par excellence are found in the economic assemblages of capitalism –under capitalism, economic flows are fascicular.

Let us revisit our example of the Federal Reserve, but by now reversing the order of direction of its distribution of flows.

We observed above that from the Federal Reserve’s sovereign determination of the supply of Treasuries to the liquidity and price of credit in money markets, from the liquidity and price of credit in money markets to the liquidity and price of credit in capital markets, and from the liquidity and price of credit in capital markets to the amount and velocity of liquidity in cash commodities markets, e.g. consumer goods markets, and so on –that this linear, pre-routed sequence testifies to operations of the arborescent model, whereby a set of the hierarchically-determined flows move from a centralized ‘link-dipole’ throughout the ‘unit-dipoles’, and in this way it is no overstatement to say that the economy is the tree, the central bank (or more generally the government) is the trunk, and the activities of the later causally radiate through and throughout the set and subset branches of the economy.

But one can easily flip this purview around by asking: “What about the contingencies of supply-and demand? Doesn’t the Federal Reserve, here always have a tiger by its tail? Are not financial asset pricing models predicated on the perpetual presence of stochastic processes, efficient markets, and value-neutrality? What about the random distribution of information (e.g. a strike in the Ivory Coast causes coffee prices to surge, a bout of bad weather causes would-be home buyers to become depressed, a group of miners accidentally discover (or not) more rare earth metals, etc.) that efficiently percolates out into the market, affecting values and effecting itself into prices?

D&G say that this is precisely what is at issue in the fascicular model –namely, whether it is not the case that now ‘the world has become chaos’, but that an image of a linear economy nonetheless remains the image of the world.[10] For this reason, if with the fascicular model a fundamental unity characterizing the arborescent mode of distribution has now ostensibly been shattered in the object-as-economy, it proves itself a false decenterment, for it is only because a higher unity now triumphs in the economy as subject: this is why no trader or analyst considers it a mere act of metonymy to speak of “how the market is feeling”, of “what the market wants”, or of how much anxiety or confidence is in the market”, and so on. When D&G observe that ‘the fascicular system does not really break with dualism…[for] unity is consistently thwarted in the object, while a new type of unity triumphs in the subject’, they are no doubt thinking precisely along such lines.

Indeed, deference to some higher unity (e.g. homo economicus, the invisible hand, marginal utility, or even behavioral irrationalities, etc.), both despite and because of the objectival disunity of centralized order is the order of capitalism. How can a system lacking any centralized command distribute its flows with any regularity, periodicity, stability, i.e. remain viable and alive? –this is the anxiety belying the fascicular model.

There are many examples testifying to this. Is it not the case that whole interbank repo market can ostensibly remain a decentered network only because it’s higher unity lies in the BBA-mandated LIBOR? That the US housing market can comprise a radicle system of heterogeneous flows only because its final unity is guaranteed by the “backstop” of the GSE’s –Fannie and Freddie? Or again, is it not the case that asset markets writ large are only ever free to operate in accordance with the impersonal pricing mechanisms of “the free market”, e.g. through competition, supply and demand, and so on, because the Federal Reserve hierarchically controls the supply and demand of money through the noncompetitive sale and purchase of Treasuries?

In finance, whenever we avert our eyes from the abstract tropes of textbooks in order to have a closer look, we always see the same fascicular tendency of final deference, a kind of openly-concealed commitment to a higher unity, belying all pretense to multiplicity: contingencies of supply-and-demand, decentralized causality, and stochastization of all price movements– in other words all of the ostensible “frees” of the “free-market”– are only ever allowed to supervene as reality on the price series of assets because the first moment of “free-market capitalism” is capitalism, a veridically-determined, hierarchically-arranged, ongoing, pervasive deference to some higher unity that perpetually ensures the equilibrated organization of its distribution of flows.

The question of market capitalism has thus always been, as D&G put it: ‘is a General necessary for n-individuals to manage to fire in unison’, i.e. is some central unity –whether bound by object (State) or subject – necessary for markets to clear, to remain stable, steady, periodic, in a steady state of equilibrium?[11] The answer and open-secret of the fascicular model has always been, in short, “yes, it absolutely is!”

However, D&G wager on a third model of economy, a third model for the distribution of flows, when they assert:

‘The solution without a General is to be found in an acentered multiplicity possessing a finite number of states with signals to indicate corresponding speeds, from a war rhizome or guerilla logic point of view, without any copying of a central order.’[12]

How, in practical terms, could this model of economy be implemented, effected and affected? In short, by way of an economy of the war machine –this is the rhizomatic model of economics.

Rhizomatic Model

‘The multiple must be made, not always by adding a higher dimension, but rather in the simplest of ways, by dint of sobriety, with the number of dimensions one always has available –always n-1…Write at n-1 dimensions. A system of this kind could be called rhizome.’[13]

Markets are multiplicities. Markets are rhizomes. The rhizomatic model of flows effectuates an immanence of markets without capitalism, which D&G call dromocracy.

Our challenge is, first, to better understand the distributive modality of the rhizomatic model; second, to grasp its qualitative differences from the two aforementioned models of economy –the arborescent and fascicular models; and third, to ask what this third model, when actualized as an economy, might look like?

To begin to address these concerns, in Chapter 1 D&G enumerate six ontological traits, or principles, characterizing the distribution of rhizomatic flows. These principles are: (i) n-dimensional connection, (ii) heterogeneity, (iii) multiplicity, (iv) asignifying rupture (or nonlinearity), (v) cartography, and (vi) decalcomania.

The reader of Chapter 1 may quickly realize that D&G’s elaboration of these principles are hyperstylized. It’s as if they’re intent to decode, or unplug the elements of each principle from their familiar technical environments. This playful tone is preserved throughout the whole of TP, while yet with each Chapter –especially up through Chapters 9 and 12 –a descriptive sobriety sets in, and the respective disciplinary origins of several important concepts become increasingly evident to the reader. However, from the outset let us understand that each of the following principles does have an original mathematical and/or scientific conceptual corollary, which we are merely introducing and defining below, but will then proceed to develop in piecemeal fashion throughout the entirety of our essay. Providing good explanations of the concepts to these principles requires patience, space, fecundity, and above all the contextual-relevance of probative opportunity. For this reason, let us briefly examine these principles below, aware of our intention to approach satisfaction of our above-stated three-fold task as we proceed.

1 and 2. Principles of connection and heterogeneity

D&G note that ‘any point of a rhizome can be connected to anything other, and must be.’ The arborescent model effectuates a stable, steady, linear distribution of flows, it ‘plots a point, fixes an order’; its flow originates from a single point, and from there ‘proceeds by dichotomy.’[14] By contrast, rhizomes, systems of rhizomes –markets as rhizomes– disseminate out in any direction, are ‘connected to diverse modes of coding (biological, political, economic, etc.)’, and nonlinearly disseminate out by coding, decoding, recoding, and back again.[15]

In a dromocracy, there’s no one big or centralized market, as such –no fixed, enclosed, total and totalizing, Euclidean, “in itself” Market. Rather a cluster of markets are populated operators who hedge-speculate-arbitrage all at once, who do so with varieties of ontologically-different assets and their respective classes of exchange, and whose invariance requirements on the economic properties comprising their assets constantly make and remake their markets on a mobile horizon of a heterogeneous, fleeting regimes of signs, weapons, and tools (technologies). We begin to explain this up in Part III, but directly and more fully in Part IV.

D&G also note that rhizomes are metricized by segments and lines, the latter of which are both actualized by, but whose actualities in turn constantly feed back into the attractors around which the quanta and flow of their metricizations unfold. We will elaborate the intraphysics of these concepts in Part III, wherein we commence our examination of the mathematical and scientific heritage of the principles of connection and heterogeneity. In Part IV, such principles are conceptually expanded further, and fitted to a dromocratic model of economy, wherein we demonstrate that nonorientable connectivity (connection) and intractable irregularity (heterogeneity) have ontologically-specific topological and fractal denotations, respectively. If one wants different financial models, a different financial economics will be required. If one seeks a different way of doing financial economics, so too a different mathematics and use of mathematics will be needed. We believe, following D&G, that topology and fractal geometry provide the requisite base set of technical tools for this financial economics, and in Part IV are prepared to prefatorily make our case.

3. Principle of multiplicity

What is a multiplicity? Definitionally, we need only observe here that Deleuze separately, and D&G together, consistently define multiplicities as becomings of objects, which, depending on textual context and relevant pedagogical task, are said to be comprised of events and affects: by the former they mean those critical spatiotemporal points in a dynamical system called phase singularities; and by the latter they mean capacities to affect and in turn be affected. Or sometimes they allude that multiplicities are assemblages of singularities and properties: by the former they again mean phase singularities, that odd, empty locus, standing at the precipice of the reshuffling of a system’s morphogenetic properties (including its attractors and basins of attraction); and by the latter they denote its intensive and extensive properties. Or sometimes they say that multiplicities are comprised of singularities and traits of expression: by the former they mean attractors, whether regular or strange; and by the latter they mean both qualities and properties (viz. “traits”), however their “expression” (i.e. whether intensively and extensively).

To streamline any ambivalence in terminology by D&G, we will say that markets are comprised of singularities and morphogenetic properties. But regardless of particularities of terminological formulae –which, for us as well, should always relate to the relevance of pedagogical task– our reader should know we intend to formally denote that dynamical set of processes that is a multiplicity in this way: Multiplicities are always composed of (a) singularities, which are those contingent but absolute hollow points around which a system’s morphogenetic properties actualize and become, around which their trajectories orbit, and beyond which the state of a system’s properties are reshuffled; but then in turn whose very materiality exogenously feeds back into, continuously remaking the absent interiority of the system’s correlative singularity; and (b) morphogenetic properties –which includes attractors, whether regular or strange, and all other properties, whether conceived of as affects, or traits of various expressions, whether intensive or extensive.

Any sustained discussion of singularities, attractors, basins of attraction, various point set properties, and other conceptual resources original to dynamical systems theory inevitably requires a level of explanation of those features affiliated with phase space. For without understanding phase space, there is no understanding Deleuze’s concept of multiplicity. We’ve conveyed the importance of our analytic commitment to dynamical systems theory (DST) to the economic wagers of dromocracy, and have also articulated our intention to include in its definition the panoply of conceptual resources of nonlinear dynamics, chaos theory, complex systems theory, group theory, topology, and differential calculus, among other tools. We will eventually observe why, when combined with D&G’s ontological schema, embedded in this expanded notion of DST resides a technically-astute but wholly radicalized notion of financial economics. However, to be clear, there would be zero possibility of any benevolent synchronicity among these respective analytics, and therefore no such subsequent wager without recourse to phase space. For only by way of the latter do we obtain the possibility of using the study of the virtual shape of a system to observe, analyze, and even tinker with a whole range of both actualized and unactualized, but always virtual and therefore very real, conditions for the behavior of that system. For this reason, a few words of explanation on phase space and its relation to the concept of multiplicity are not unwarranted herein.

A system whose variables are preserved but otherwise change in time will either move within a boundary of space, or else will fly off to infinity. The state of the variables of a system (i.e. its morphogenetic properties) are represented in phase space, wherein information about the system (for instance the velocity, position, and so on, of a ball projected in physical space; or the delta, time-decay, and so on, of a financial derivative approaching its maturity in economic space) is articulated by a coordinated set of points. As the system evolves, some points may reposition in phase space, while some may remain invariant. As the system continues to evolve and varieties of points continue to change or remain invariant, careful examination of that phase space will allow us to map their trajectories, and a virtual image of that system, unexhausted by its actuality, will emerge. For a fairly simple system, its shape may be a straight line: here, we will know it is Euclidean and linear; or some type of curved surface: here, we will know it is Euclidean and has low-level nonlinearity. A more complex system, by contrast, will make a manifold –or in Deleuze’s terms, a multiplicity.

Chaos theory illustrates that already phase space portraits in two dimensions exhibit surprising behaviors. However, with the addition of each variable (sometimes also called ‘parameter’) in phase space another dimension is added, and with the addition of each dimension so too is added another ‘degree of freedom’. As spaces of three, four, five, and more dimensions are added, and subsequently high-parameter system dimensionality is attained, one increasingly edges towards the concept of a complex of infinite degrees of freedom, highly nonlinear, nonorientable, irregular, suffused with high-order turbulence, and deterministically-chaotic. This is Deleuze’s true conception of a multiplicity.

We will see that dromocracy, in essence, is founded on infinite of degrees of freedom for its operators. Its institutions are highly nonlinear, nonorientable, irregular, suffused with high-order turbulence, and deterministically-chaotic. If markets are multiplicities, and multiplicities are rhizomatic, it is crucial that we understand what this means for the ontology of markets –namely, of what it means that markets, as D&G say, ‘are defined by the outside’, and yet never have ‘available a supplementary dimension over and above its number of lines’;[16] which is to say that they are a kind of pure exteriority without overdetermination, a mechanism-independent mobile structure to the space of exchange. We will elaborate more fully the profound dynamics of multiplicities, their relation to phase space, their nonlinearity, and its consequences for dromocracy immediately below, and then more fully in Parts III and IV.

4. Principle of asignifying rupture

Nonlinearity is the rule of cause in rhizomes. Linearity is an occasional exception, a subset of the more general class of causality that is nonlinear. For this reason, D&G caution against surreptitiously importing a conservative concept of (linear) causality into our image of economic flows, when attempting to think the rhizomatic dynamics of markets. For ‘[a] rhizome may be broken, shattered at a given spot, but it will start up again on one of its old lines, or on new lines…Every rhizome contains lines of segmentarity according to which it is stratified, territorialized, organized, signified, attributed, etc., as well as lines of deterritorialization down which it constantly flees.’ It is true that ‘[t]here is a rupture in the rhizome whenever segmentary lines explode into a line of flight’. However, it is also the case that ‘the line of flight is part of the rhizome’ itself.[17]

With the principle of asignifying rupture, D&G are therefore urging their reader, let us not to underestimate the profound consequences of nonlinear causality, and with it our expectations about the material capacities of markets, or of their role in the design of a war machine economy. That markets, at their essence, as we will see in Part IV, are assemblages of operators-assets-exchange; that such assemblages comprise the hyperfungible rhizomatic institutions that ultimately effectuate nomadic distribution; and that such institutions, as we explain, are best actualized as local clusters of exotic options (CEOs), which are then globally-enfolded within a universal synthetic CDO (USCDO), and together comprise a H20fall economy –this does not immediately reveal to us that any nonlinearity necessarily prevails. Rather, this is something our reader will need to be shown. D&G’s emphatic association of high-level nonlinearity with a war machine economy, however, is not easily overvalued. For this reason, we will briefly establish the ontological differences between linearity and nonlinearity immediately below; and then in Part IV, will be free to develop a fuller, less-prefatory exposition of its importance.

So common today is the method of calculus in financial economics, one might occasionally forget that most differential equations have no single solution. Of course, if we do forget this, it’s because the solvable equations are those which most often show up in our textbooks –by which we mean linear equations, and those rare classes of nonlinear equations prostrating themselves under compulsions of techniques for their solution. This is rendered both ironic and more than ironic by the fact that orderly, solvable, linear systems are anomalies, while nonlinear systems are the rule. Why does this matter? To begin with, our image of a linear world is interwoven with presuppositions involving proportionality and additivity, under which the principle of superposition always holds. Because linear relationships are proportional and additive, they can always be plotted along a straight (Euclidean) line on graph. For this same reason, a deep, conservative constancy marks the volatility of a linear system. Its equations, linear equations, permit the disassemblance and reassemblance of their parts with no material effect: one can subtract and add them up, but their numeric values always will retain their Euclidean identity, for while the principle of additivity prevails, no true change is possible.

Nonlinear equations, by contrast, are either not reducible to a single stable solution, or admit no solution whatsoever. Such equations articulate relationships that are strictly disproportional, which means that nonlinear phenomena are neither additive nor isolable, their parameter behavior is nonconstant, even their volatility is nonconstant.[18] Moreover, operating on nonlinearities can qualitatively alter the basic character of their rules of combination –indeed the defining feature marking a complex nonlinear system involves the ever-present possibility that some small, imperceptible, often ostensibly-insignificant change in one parameter might push an otherwise conventional, even apparently stable system across a singularity, ushering in a qualitatively new and very different behavior.[19]

What profound material capacities do the denizens of a dromocracy horizontally wield by virtue of their operation on and with high-parameter nonlinearities? Already in Part III we will see that nonlinearity poses a radical challenge to the very principle of classical representation, on which our panoply conceptions of economic value, i.e. cardinal value, which comprise all prior theories of cardinal of value, are implicitly predicated. In opposition to cardinal value D&G outline an ordinal concept of value. This matters for Part IV, wherein we will deepen the (ordinal) plot of our story –moving from Part III’s expository discussion of the relation between the ordinal concept of value and quintessential abstract formulation of an ordinal process of becoming that is the Cantor set, to now in Part IV, its use in constructing a Koch curve: and from this vantage, our reader will grasp that the concrete deployment of the Koch curve is the modus operandi of the proliferation of clusters of exotic option (CEOs) –which realizes an infinite growth of economic length in a finite volume of space (That the ethic of infinite growth of volume is to be replaced with an ethic of infinite growth of length in a dromocracy will become clear at this time as well).

Admittingly, we have highlighted only several of the many profound material capacities of nonlinear causality for the financial economics of dromocracy in Part IV: for example, that in a dromocracy nonadditivity unseats superposition; that the denizens of a dromocracy act as operators who themselves act as a critical stimuli, the control parameter, which “switches on” nonlinear phenomena, so to speak, thus disposing the system of multiple solutions whose availability remained yet unactualized but virtual, and from which its denizens are free to choose; that dromocracy operates by way of involution, which already problematizes the arborescent ethic of strict natural selection –and that even when the latter is operative, heterogeneities of aparallel evolution and “unnatural” symbioses are far more general phenomena than any tree-like descent, genetic overdetermination, or pseudo-Nietzschean fantasies of uber-fitness, the latter of which always seem to trickle into and then leak out again of our anthropomorphized biologism, and on into our models of economy. We believe these are merely a few of its possible trajectories. At any rate, nonlinearity is the concept we should understand as being convoked by D&G when itemizing the principle of asignifying rupture.

5 and 6. Principle of cartography and decalcomania

D&G’s commitment to the principles of cartography and decalcomania should not be interpreted in a spirit of metaphor, nor as a kind of poetics, nor as synecdoche. D&G literally mean cartography and decalcomania. With these two principles they intend to denote the activity of map-makings of phase space, and then placing its variables into a state of perpetual variation.[20] We introduce this notion below, and then more fully take it up in Part IV.

We observed above that analytic techniques applied by DST to phase space lend us a powerful method for transmitting numbers into images, of abstracting the singular and virtual from the ordinary and inessential, of extracting information from becomings of trajectories, and constructing n-dimensional maps in order to tinker with the unactualized possibilities always already virtual in a multiplicity.[21] It is thus never a question of tracing and reproducing, but rather of mapping and decalcomania. D&G assert that ‘[a]ll of tree logic is a logic of tracing and reproduction.’[22] They therefore oppose to the overcoded activities of tracing the decoding activities of mapping; and for conservative operations of reproduction they wish to substitute radical operations of following –of submitting to an event, of becoming worthy of the singularities in matter; of following matter, as an operator or set of operators follow the contingencies of the real, as an artisan follows the plane of wood she planes; of always examining and thinking, following and tinkering, following and tinkering, following, thinking, following and tinkering: perpetual modification with the map, putting into constant variation its decals. The map may be in incessant flux, it may testify to chaos, to turbulence, or the special condition near total chaos we will come to know as far-from-equilibrium. But we will show in Part IV that in fact this is the very condition of possibility of economic health, the very condition for a rhizomatic distribution of flows, the very condition for dromocracy.

The denizen of a dromocracy is an operator. The operator is an artisan. And as such she always seeks to operate on and with and by matter, experimenting with its divergent evolutionary capacities, of loving, respecting, and coaxing, but always demanding more from matter, i.e. of more than what matter even knows itself to be capable. The operators of a dromocracy are cartographers, decalcomaniacs –and thus, as we will see in Part IV, are hedgers-speculators-arbitragers all at once– always following a line of flight, submitting to singularities, perpetually reaffirming their self-made becomings of fate with affirmation and joy.

Let us move to the task of Part III.

[1] For example: ‘Rather than operating by blow-by-blow violence, or constituting a violence “once and for all,” the war machine…institutes an entire economy of violence, in other words, a way of making violence durable, even unlimited.’ Ibid 396 Moreover: ‘The State has no war machine of its own; it can only appropriate one in the form of a military institution [read: capitalism], one that will continually cause it problems.’ Ibid 355

[2] Ibid pg. 5, 16

[3] This term denotes something very specific for D&G, which we address when we concern ourselves in Part III with Chapter 9.

[4] Pg. 16

[5] Pg. 16

[6] “The Hand of the Lever”, Nicholas Lehman, The New Yorker, July 21st 2014 pg. 47

[7] Ibid pg. 45

[8] Ibid pg. 5-6

[9] Ibid pg. 5

[10] Ibid pg. 6

[11] Ibid pg. 17

[12] Ibid pg. 17 {my emphasis}

[13] Ibid pg. 6

[14] Ibid pg. 7

[15] Ibid pg. 7

[16] Ibid pg. 9

[17] Ibid pg. 9

[18] In Part IV we will later to the significance for financial economics that the signature of nonlinearity is the volatility of volatility.

[19] Nicolis nicely captures the basic ontological difference between linear and nonlinear systems, observing, ‘[i]n a linear system the ultimate effect of the combined action of two different causes is merely the superposition of the effects of each cause taken individually. But in a nonlinear system adding two elementary actions to one another can induce dramatic effects reflecting the onset of cooperativity between the constituent elements’ –that is to say, a cooperativity and set of subsequent material capacities that were previously lacking. ‘This can give rise to unexpected structures and events whose properties can be quite different from those of the underlying, elementary laws [i.e. governing linear systems], in the form of abrupt transitions, a multiplicity of states, pattern formation, or an irregular, markedly unpredictable evolution in spacetime, referred to as deterministic chaos.’ G. Nicolis, Introduction to Nonlinear Science, Cambridge University Press, 1995 pg. 1

[20] (‘The search for laws consists of extracting constants even if those constants are only relation between variables (equations). An invariable form for variables, a variable matter of the invariant…[By contrast is] nomad science [wherein] the relevant distinction is material-forces rather than matter-form. Here it is not exactly a question of extracting constants from variables but of placing the variables themselves into a state of continuous variation.’) TP pg. 369

[21] Gleick describes ‘phase space…[as] one of the most powerful inventions of modern science…In phase space the complete state of knowledge about a dynamical system at a single instant in time collapses to a point. That point is the dynamical system –at that instant. At the next instant, though, the system will have changed, ever so slightly, and so the point moves. The history of the system time can be charted by the moving point, [mapping] its orbit through phase with the passage of time.’ Gleick pg. 134

[22]