From Bearer Bonds to the Blockchain: Artistic Perspectives on Digital Money

Bitcoin and the blockchain have generated an enormous amount of press, as well as investment by governments, banks and technology companies. Ruth Catlow of Furtherfield  and Ben Vickers of Serpentine Galleries, with the generous support of the Austrian Cultural Forum London organised a fantastic workshop attended by artists, representatives of public and commercial arts organisations, and technologists. The agenda was to consider what the blockchain, a poorly-understood yet politically-charged technology that means many things to many people, might mean for art and artists, and society-at-large.


Although our audience had a specifically artistic interest, the discussion around blockchain intertwines economics, technology, and public policy, so I thought it might help to take a step back and start by thinking about money pre-bitcoin. Specifically, I wanted to un-entangle some of the philosophical and historical questions around money; not least because the nature of money itself, and long-standing assumptions in Western economies, are today being subverted by the ongoing after-shocks of the 2008 financial crisis, to wit: negative interest rates, the potential phasing out of cash, and financial repression.

Money as Social Construct

I see money as a social construct, or alternatively, a de-centralised social contract with few explicitly articulated constraints on the individual, but plenty of implicit conventions-in-use. The essence of this contract is that money gives its holder a claim on assets or labour. It generally implies at least two parties in any given transaction; as well as a belief system that most parties in the given society mostly agree upon. These ways we use money are diverse, but are closely related to metrics for the utility of the money in question: authentication, anonymity, portability, convenience, legal certainty and fungibility.

Some examples may help.


Cash appears to be the simplest form of money. U.S. Dollars represent a claim on the American Treasury via the Federal Reserve Banking system. Since dollars are no longer backed by gold reserves – in other words, if one goes to the Fed or Treasury with a briefcase of dollars, one is not generally entitled to an equivalent amount of gold coins in return – this claim on the U.S. is termed fiat money. That is, most people, domestically and globally, agree that the Fed, and therefore the Treasury, is good for its dollars, and that everyone else in the system will provide goods and services against dollars. Furthermore, most people agree that the Fed will run the U.S. economy in a reasonably responsible way – though this consensus is far from unanimous. When, and if, this confidence erodes substantially, one may see devaluation, or inflation, depending on how the relative price of dollars to foreign currency, or to domestic goods/services, respectively, have changed. A recent example on how belief systems regarding money can change: during the summer 2015 EU crisis when Greece looked likely to be ejected from the Eurozone, there was much serious talk on how a parallel currency could co-exist with the Euro (the so-called ‘New Drachma’).

Cash is more or less anonymous in use, often is free of record/receipt, and may be irreversible (i.e. no refunds). The central bank doesn’t generally keep a ledger of individuals or businesses that hold modest amounts of cash; they do keep a ledger for commercial banks, which have a special relationship with the central bank. The central bank also closely watches how much cash is in circulation on an aggregate basis (so-called M0 or base money) and monetary policy is the science, and art, of managing M0 (and its friends M1-M4), in order to meet various legislative or statutory goals: often, price stability and low unemployment. The anonymity of cash is one reason it is interesting for tax evaders and tax authorities alike. As an aside, for all the noise about offshore accounts in the Panama Papers, HMRC estimates £16.5BN of lost UK tax revenue actually comes from VAT evasion – i.e. paying one’s plumber in cash, an entirely British affair that has nothing to do with offshore centres.

The authenticity of cash is verifiable in a relatively de-centralised way, in a reasonably short period of time: an experienced eye can spot most counterfeit bills, and marker pens or UV lights can easily be used anywhere.  Cash is portable, yet is purely symbolic – for the most part, the social contract that underpins cash, isn’t spelled out in other than the most terse terms on a bill. Most of the enabling legislation, case law, and so forth, exists outside the cash note. These points will become important later in the blockchain section.

It’s worth noting that many of the features above, which fall under the rubric convenience, mean cash can also be stolen easily and thus is expensive to store, transport, and insure.

Precious Metal

I will intentionally not say much about gold and silver, as the history and cultural aspects, while fascinating, would hopelessly complicate the discussion. Indeed, most respectable commentators hold that gold is a ‘barbarous relic’ (as John Maynard Keynes’ put it in 1923) and should be consigned to the bejewelled dustbin of history. Suffice it to say: gold is anonymous, reasonably portable (relative to value), easily authenticated, requires no ledger, but like cash, is expensive to protect. As above, gold relies on an obscure social contract and judging by the price action, I’m not sure the consensus on gold’s value hasn’t changed. Gold also may suffer from the nasty habit of being declared illegal just about when it might prove useful, due to inflation or war – for instance see Executive Order 6102, signed in 1933, that criminalised private ownership of monetary gold during the Great Depression.

Bank Deposits

In contrast to the above, money sitting in a bank has no material form, until it is pulled out of an ATM. It sits in the bank’s ledger, and definitely belongs to someone – namely, the depositor. Thus it is not anonymous, and is, in the absence of fraud or error, authenticated. Nor is it portable, though one can transfer deposits to another bank.

Bank (time) deposits do, however, earn interest , while cash obviously doesn’t. More accurately, they used to earn interest – in what some will call financial repression, and others, unconventional monetary policy, retail deposits in most Western nations, and Japan, earn near-zero interest. In an increasing number of situations, certain deposits now earn negative interest rates – one pays the bank to place a deposit.

Bank deposits also exhibit double counting. In its first guise, double counting is more commonly known as fractional reserve banking. Basically, very little cash money actually exists in the banking system. A great deal of the ‘money’ in circulation is in the form of on-demand deposits at various commercial banks (so-called M1). But those deposits rarely become cash. Bluntly, when a mortgage bank disburses a loan to a home-buyer, it almost never pays out hundreds of thousands of pounds in cash; rather, there are a chain of debits and credits, respectively, of the buyer and seller deposit accounts, that result in the seller’s account going up by the price of the house. The bottom line, for the financial system as a whole, is that a tiny sliver of M0 cash supports a large volume of M1 deposits. A bank run is when all depositors want their cash out of the bank at the same time, and there isn’t enough to go around.

A more relevant example of double-counting is when a transaction actually happens, there is often a period of 1-3 days, when balances are in transition between the seller’s deposit account and that of the buyer. Again, there are a chain of transactions, often involving two or more banks (i.e. the seller’s and buyer’s), as well as the central bank, during which time deposits may well be double-counted in the accounts of multiple financial institutions. This is mostly fine, because the central bank, in theory, supervises the system, provides plenty of extra cash liquidity and, in any case, the double-counting doesn’t last for very long; however, when there is a financial crisis, this could become a problem. This double-counting problem applies to blockchain precisely because the latter is basically a simultaneous system – transactions are confirmed and settled almost instantaneously.  I would point the reader to Izabella Kaminska’s writings over at the Financial Times for more on this topic, and in general for excellent critical commentary on how various quasi-utopian aspirations of digital money square up to the sometimes brutal realities of the financial world.

Bonds and Shares

The last animals in this taxonomy are bonds and shares, of which I’ll only treat the former. Bonds combine many of the features above, namely they are a promise (i.e. debt) by a party (the issuer) to pay another party (the bondholder) in a certain currency (dollars, pounds, etc.) at a certain rate of interest (known as the coupon) on a certain date (the maturity date of the bond).

The first difference we note is that bonds have a maturity date – unlike on-demand deposits, the bondholder generally can’t get his/her money back whenever he/she wants. So they look more like time-deposits in a bank (which incidentally go into M2).

Bonds, interestingly, used to come in two flavours: bearer and registered. Registered bonds usually have no physical form: rather they are an entry on the ledger of a central record-keeping agency, a so-called custodian. There is usually a specific method of transferring them, through a so-called clearing system – basically this is the bond-world equivalent of the bank that kept track of who had what deposit, and provided a way of transferring money between deposit accounts. Bearer bonds are more interesting – they belong to whoever physically holds the bond document and therefore are anonymous. That owner can transfer the bond to another by simply giving the transferee the document. Bearer bonds used to have little pieces of paper attached to them, called coupons, that one tore off and took to the bank, where one could get cash in return for the coupon. So bearer bonds actually look a lot like cash. They are mostly extinct now, since they were often used for tax avoidance or evasion. Also, if one misplaced a bearer bond, the wealth that it represented (for them) was often lost, disappeared, gonzo…

Bonds as a class have a particular relevance for blockchain – the ‘system of beliefs’ that govern how they work are mostly contained within the bond document itself, in hundreds of pages of legal language specifying how the bonds are to be transferred, what happens if the bondholder defaults on their payments, which courts are allowed to resolve disputes between bondholders and issuers, and so forth. However, in order to enforce contractual terms or resolve a dispute, a bondholder needs to approach the issuer or chase down the custodian/trustee, and if that doesn’t work, sue everyone – all of which is a time-consuming and expensive process.

Bitcoin, the Blockchain, and Digital Money

After that lengthy preamble, we can perhaps see, in the proper perspective, what bitcoin and the blockchain might offer to various societal stakeholders. Firstly, terminology: bitcoin and the blockchain are easily conflated, but for the purposes of this essay, bitcoin is a ‘digital currency’, while blockchain refers to a complex of underlying technologies that support and enable bitcoin and other digital currencies. Blockchain-based platforms may be available to everyone (public) or only accessible by a specific group of users (private). Bitcoin has attracted a great deal of attention and notoriety, but I, mirroring the FF/ACFL conference, will concentrate on the blockchain, which also happens to be the focus of intense investment by technology firms, venture capitalists, banks, and regulators. Furthermore, I will wave my hands and abstract away exactly what the blockchain is. Suffice it to say that it replaces the central ledger or repository variously referred to above, with a distributed ledger which is held at various nodes in a network, in multiple, synchronised copies. Every time a transaction happens, this information about asset ownership is updated across the network (essentially) simultaneously. Most of the complexity arises in authenticating transactions and in working out the time order in which transactions have happened, to avoid double counting/spending, ensure anonymity, reward the various agents in the network for participating, etc.  An engaging lay explanation of bitcoin (blockchain is easier to grasp if one starts with bitcoin) is here.  A sophisticated, but not especially mathematical, explanation of the blockchain, which starts with bitcoin’s implementation of the blockchain, is here.  For those interested in the undressed guts, see the Nakamoto PDF below which references Hashcash and other bits of prior work in this area.  Lastly, I’d be remiss in not pointing to the blog of he whom some, depending on their cultural background, might deem the Pretender, the false Dimitry, or a mere Anti-Pope: self-outed as Satoshi Nakamoto.

Smart Contracts

One of the most exciting, from a commercial perspective anyway, things about the blockchain is the idea of a ‘smart contract’. As I touched on above, bonds have fixed contractual provisions but in order to enforce any of them, one needs go to court or to a custodian. What if there was a bond which would automatically do certain things, like pay its coupon, or shorten its maturity date, in such a way that the (small) bondholder didn’t need to go fight the (big) issuer in court? A real-world example arises with Everledger diamonds that have blockchain-derived serial numbers etched onto them, accompanied by smart contracts that describe their provenance. One of the important points to note about blockchain, posited early on by bitcoin’s (ex-)pseudonymous inventor Satoshi Nakamoto, is the idea of immutability – once a transaction is inserted into the distributed ledger, it is impossible, or unfeasibly hard, to reverse. This means, in a contractual, financial, and legal sense, the history and provenance of diamonds (say Angolan or stolen) cannot be re-written or laundered. Another of Nakamoto’s principal aspirations was that, in a manner analogous to authenticating cash, authentication and verification of blockchain-based transactions should be something that could be done easily by an agent, even if they weren’t technologists or didn’t have the resources of a network node (i.e. a farm of computers mining bitcoins).

Devolving Funding, Ownership, and Contract

Smart contracts may also allow groups of (not necessarily rich or especially knowledgeable) collectors to jointly buy stakes in an artwork that none of them could have afforded singly. A digital contract would accompany the artwork, and the collectors would be immutably bound to that artwork. Conversely, the artist too could be immutably bound to the work, so that, in 30 years, when it sold at auction for millions, the artist could get paid. This is in contrast to the current situation, where artists or early-stage collectors don’t always benefit from the eye-popping gains in the value of artwork they created or nurtured.

It is however, important to point out that the issue I highlight above is not essentially technological – it is a contractual problem. Nothing actually prevents groups of collectors buying shares in paintings, just as nothing prevents artists from selling artwork with a restrictive covenant that constrains further sales or attaches to such  sales (and plenty of artists have explored these ideas of contract-in-art). The practice isn’t widespread presumably because few collectors would buy an emerging artist’s work with such a proviso. Having blockchain technology doesn’t really change the picture, in my view. What blockchain does do is automates execution of the relevant provision, and in the event there is a breach or dispute, might lower the cost of enforcement. Because smart contracts don’t require lawyers or court enforcement, and are almost instantaneous to execute, they become useful for relatively small sums of money. The diamond example above can easily be ported to art: Ascribe and MONEGRAPH provide content management suites that use blockchain to manage rights to digital art assets.  The notion of lowering barriers-to-entry is one of the most prosaic, and therefore most adoptable, applications of blockchain.

A high-profile applications in the area of funding and rights management was by the musician Imogen Heap, who has established Mycelia, a music storage and rights-management system built upon the Ethereum platform. Mycelia hosts an artist’s tracks, automatically updating as and if new and improved recordings are added; the information is stored in the cloud, and as a track is played, a smart contract is triggered to automatically pay the artist. Mycelia would also store other digital assets, such as liner notes, videos, etc., and contain provisions to allow derivative use: content to be embedded into other media (such as videos, advertisements, etc.) would trigger automatic payment to the artist. In theory, this all happens in the music industry already, but I suppose the point is that middlemen or artists’ agents handle the process, often badly (from artists’ perspective) and take a significant slice of the economics. In Heap’s words, Mycelia’s promise is that it might make the contracts between music artists and whoever ultimately is paying for content, whether record labels, advertisers or the public, much more transparent, easier to understand, self-executing, and thus, cut out layers of middlemen, while ensuring artists received as much revenue as possible, as quickly as possible.


It appears that Heap’s ideological perspective is that audience, listeners, can and almost should be brought in as partners with the artists, and thus Mycelia allows for more direct links between the two. An analogue of this forms the curatorial practice of Helen Kaplinsky, who talked about how to share assets in the current British cultural climate, where the concept of ‘civic publicness’ is crumbling, throwing into crisis the Enlightenment-era model of the museum as a public good. She has been converting a cultural space from a single-landlord entity into one that is owned by a community land trust. In a related project, she wanted to think about how artworks, accessioned into institutions but not currently on display, may still remain in circulation (and visible) rather than just sitting in a warehouse. In her vision, viewers, artists, and institutions would share an artwork in a fundamentally different way than the previous institutional model, which was binary – either a work was on-display or in-storage. More generally, the project tries to address questions that are coming up now in the contemporary economy & in art, revolving around what to do with artwork that might not have a ‘permanent’ or ‘stable’ state, something that has become key in museum conservation departments globally. Blockchain-based platforms like Ascribe provide a way of keeping track of interactions (ownership, borrows, licensing, insurance, liability, etc.), and because of the relatively low legal/financial cost, perhaps enable large-scale sharing of an artwork or a collection. Again, incorporating blockchain seems to me an incremental, and possibly worthwhile, technological improvement to an existing real-world solution: at MIT, students are already able to borrow artwork for their residence rooms.

Geo-wallets: Monetising the Self

Another intriguing applications of the blockchain lies in the integration of money, via the digital wallet, with GPS technology. Max Dovey presented a project undertaken with University of Edinburgh’s researcher Chris Speed where geo-location technology was connected with a digital wallet, such that the account balances within the wallet would change depending on how the user/viewer moved through Edinburgh. Another project called Handfastr also meshed geo-location with digital money, allowing couples to form temporary fake ‘marriages’ and temporary pooled accounts based on proximity: as long as the couple were near each other, they would have a joint digital wallet, and when they moved apart (spatially) they would revert to individual wallets.

These projects exemplify how small collaborative groups, physically co-located, can self-organise, and pool their financial resources easily and with a minimum of legal and contractual overhead.

In my view the more interesting perspective is an ambiguity of the whole thing: by linking money so closely to other digital technologies (GPS today, and in the future, say, bio-medical data from an Apple Watch), the move towards monetising individual identities and bodies continues apace. At a basic level, one can imagine large corporations, and the state, having even more information and potentially, control, over people. Given the enthusiasm with which people have adopted cashless, non-anonymous, immutable-record and friction-free payment methods (tapping debit cards, Apple Pay, or Uber), I can imagine many people will happily opt-in to linking more and more elements of their identity into a variety of surveillable and monetisable, albeit ‘free’ and convenient, networks.

From Self-Executing to Self-Replicating

Most of the approaches above have looked at funding, ownership, and sharing implications of the blockchain. Another potential artistic trajectory could be investigating the underlying technology itself. For instance, Plantoid is a system implemented on the Ethereum blockchain, that takes the initial form of a sculpture; however, once a certain trigger, described in an Ethereum smart contract, is reached, the blockchain instructs human collaborators to make a new version of the sculpture (and an algorithm embedded in the smart contract provides the specific dimensions of the sculpture to the human producers). The auto-generative potential, even if it is, at the moment, human-assisted, is combined with an economic metric, as encoded in the smart contract. If one takes a dystopian view, the project, loosely paralleling certain concerns about hypothetical self-replicating AIs, perhaps shows a future where mechanical things make themselves over and over, with human beings as mere workers or artisans operating under the (benevolent?) guidance of the an automated, financialised network.

Questioning Some Shibboleths: Доверяй, но проверяй

In the FF/ACF discussion, the word ‘trust’ kept coming up.  All the while, I was reminded of U.S. President Reagan’s little joke phrase he’d trot out regularly at his meetings with General Secretary Gorbachev: “Trust, but verify”.

In Nakamoto’s original technical paper, in which he drew up the bitcoin idea, he quite explicitly describes it as a system not predicated on trust. Specifically, it doesn’t require participants to trust the keeper, whether governmental or corporate, of the central ledger, as was the case with bank deposits or bonds. In fact, the technology makes distinctly non-idealistic assumptions: rational actors, often intensely individualistic even quasi-autistic, who don’t know each other, thus have no reason to trust each other or any third party.  Hence the importance of ensuring that each transaction can be authenticated and verified independently and quickly.

Other words came up in our discussion: ’emancipatory’, ‘radical’, which appear to be sentiments that come in from the hype around bitcoin. A cursory Google search tells us bitcoin and other crypto-currencies would eliminate the need for governments, central banks, courts, international law. Many of these aspirations seemed to gloss over the point that bitcoin doesn’t operate in a vacuum, it needs telecom networks and lots of computers, and in most cases, it interacts with real world laws and regulations. These quasi-public goods represent a societal subsidy (or shackle), often by profit-maximising evil capitalists and neoliberal-infected governments. Moreover, even self-executing ‘smart contracts’, pace theory, are unlikely to do away with disputes or fraud. What about when the system makes a mistake or simply breaks? Just as in the real world, we keep a wary eye on cash wallets, in the digital world, there will presumably be a need for users to constantly monitor digital balances, as well as familiarise themselves with applicable Terms & Conditions (which most of us currently Ignore & Accept). When something bad happens, counter-parties may, in extremis, need to resort to boring physical-world things like courts, lawyers, and contracts. As an aside though, Vitalik Buterin, the main force behind Ethereum, has proposed a ‘decentralised court’ that would arbitrate disputes.

My view, and I think that of some in the FF/ACFL room, was that the blockchain technology isn’t inherently emancipatory, just as it isn’t inherently repressive. As Vinay Gupta pointed out, blockchain can be used to support pretty much any political outlook. In fact, the reason banks are interested in it is pretty tedious stuff: it might dramatically shorten the amount of time it takes to finalise transactions in bonds, stocks, and other financial instruments. It might also minimise the risk of double-counting money or assets during the payment settlement period, as mentioned above. Similarly, governments are interested in blockchain because it might reduce tax fraud, make for a safer financial system, better track eligibility for welfare support, and increase employment.

Steve Fletcher at Carroll/Fletcher Gallery noted the ecological cost associated with implementing blockchain – again, hardly something that fits comfortably in the radical story-line. The ecological cost arises from the electricity utilisation of thousands of computers that, collectively, form the network which underpins the distributed ledger. These computers are constantly running to process transactions, a process sometimes called ‘mining’ (analogy with mining gold), and this eats up lots of power.

At a poetic level, insofar as economics can be looked at poetically, this process, called ‘proof-of-work’ in the blockchain jargon, is a loose analogy to what I originally defined money as: a socialised claim on labour (or assets). Hence, it would almost be philosophically perverse to expect a form of money, digital or physical, that did not perform this almost-sacramental act of abstracting labour into monetary value.

From another perspective, and this lies beyond the scope of this post, I’m also not sure how scalable the various blockchain technologies are – if everyone in the world used blockchain for all transactions, does that imply a huge increase in mining processes (with consequent ecological cost), or can a very limited stream of proofs-of-work be used to support all transactions? While blockchain might reduce the need for trust (in government or big corporations), it does so tortuously and expensively; I can’t help sensing a vague analogy with American survivalists who flee the Federal government for a rural homestead, armed-to-the-teeth and stocked with tinned provisions, bleakly awaiting the End of Days.

In summary

The FF/ACFL programme was a great opportunity to bounce ideas around, without a tightly-framed artistic, commercial, or ideological agenda. What I’ve tried to do here is sketch out how one might think about money generally, using the metrics of authentication, anonymity, convenience, fungibility, and contract, and apply these metrics to the bitcoin/blockchain complex. What seems to emerge is a potential for blockchain to devolve mechanisms and processes for funding for artists, as well as allowing various players in the arts ecosystem – artists, collectors, viewers, curators, and others – to define how they want to interact, with the possibility that sharing and artwork almost merge, or at least become as two sides of the same coin. Both of these potentialities seem more evolutionary than revolutionary. Other approaches offer fertile ground for exploring bio-politics and auto-generative physical artworks. A constant I observed through the entire conference was the inherent ambiguity of the technology: in contrast to the original libertarian or revolutionary claims made for bitcoin, the evolution of the technology today seems to offer as many risks of a dystopian future as emancipatory opportunities.

U. Kanad Chakrabarti  is an artist and former banker based in New York and London.


Tauba Auerbach at Paula Cooper: Sexy Glass Meets the Mathematical Sublime

What started as a review of Tauba Auerbach’s current show at Paula Cooper led to the question of how indeed a successful work of art might engage with mathematics – what might be some approaches to visualising abstract and often inaccessible concepts?

Tauba Auerbach The New Ambidextrous Universe (2014) Source: ICA

Prior to seeing the New York exhibition, I visited the artist’s 2014 show at London’s ICA, The New Ambidextrous Universe.  In London, Tauba Auerbach exhibited about 7 objects, made of plywood, glass, perspex, and powder-coated steel.  The objects, smooth-surfaced and minimal, yet elaborately turned and possibly machine-made, looked sort of like useless furniture.  Formally, they were united by a concern with chirality: some carried a right-handed orientation, others left, while (and here my memory may fail me) a glass piece demonstrated a similar idea through light-polarisation.  Despite, or perhaps because of, the show’s sophisticated intellectual premise, I found myself oddly un-moved by it – there was no punch to the gut.  All I saw was reasonably nicely-made objects on low long plinths, in designer colours – stuff that would look great at Heal’s or an expensive Knightsbridge condo, and definitely looked like what art is supposed to look like.

Tauba Auerbach The New Ambidextrous Universe (2014) Source: ICA

Reading interviews with the artist, it’s clear that she has a fascination with the idea of maths, and while that undoubtedly finds its way into the work, I felt her pieces added but little to my understanding, or even appreciation, of chirality or of the eponymous book by the late Martin Gardner.

Tauba Auerbach Projective Instrument (2016) Source: Author’s own image

Her current exhibition, Projective Instrument is also built around a book, this time by an eclectic American architect, Claude Bragdon, whose interests spanned higher-dimensional geometry through to Theosophy.  The exhibition had a number of her trademark objects, made during a glass residency, as well as woven paintings.  These, or similar, paintings unfortunately were displayed to much greater effect, alongside Charlotte Posenenske’s work, in the gorgeous rooms of Indipendenza Roma  (2015).  The Paula Cooper show also featured seductively-coloured paintings made with custom-made implements ‘inscribing patterns derived from chain-maille, fractal curves, and four-dimensional tilings into the paint’ (press release).  At the end of the day, however, they were pretty simple, inoffensive wall decorations that neither illuminated the mathematics nor particularly pushed the boundaries of artistic practice.  Auerbach’s imprint, Diagonal Press, was, if anything, more interesting, showing copies of Bragdon’s book, amongst others.  I couldn’t tell if they were for sale, or if they’re thrown in gratis if one spends (apparently) $150,000 on a painting.

Tauba Auerbach Projective Instrument (2016) Source: Paula Cooper Gallery
Tauba Auerbach Projective Instrument (2016) Source: author’s own image of ‘library’ at Paula Cooper Gallery

A second take on maths-in-art comes from Falke Pisano’s rather good show at Hollybush Gardens (London, 2015), entitled The Value in Mathematics.  Pisano’s approach was more cerebral, less apparently infatuated with maths: in fact, there was very little about maths per se.  It was more about the teaching of mathematics, and how the subject is presented in society.  The exhibition consisted of a number of flat works, sculptures, and videos.  The flat works seemed to be unified by descriptive texts or titles on the wall, while the sculptures had in common an open structure, relatively humble or light materials, and open plinths.  For me, the overwhelming aesthetic was that of Modernism, of graphic design from a pre-computer era.  However, on closer viewing, particularly of the prints, the organising principle revealed itself: the various prints described what could be characterised as systems of valuation or exchange.  What animated the exhibition were the videos which, curiously, brought a more human and less conceptual feel to what could have been a cold and information-heavy exhibition.  Only at the end did I read the press release, and worked out the political sub-text of the show: as I understand, it challenges the impression, apparently promulgated by mathematicians, that mathematics is somehow objective and ‘value-free’, whatever that means.  The exhibition proposes that the teaching of mathematics makes it inherently political, context-dependent, and hierarchical.  Whether one thinks Pisano’s particular programme is interesting or not, her handling of the material is deft, a collage of politics and the scientific, woven into a fictional system of thought, perhaps intentionally layered, obscure, even obtuse [1].  I found Pisano much more convincing than Auerbach, where the maths seems just grafted onto a high-end design practice in order, one might surmise, to lend gravitas.  At a presentational level, I liked the fact that Pisano’s show gave the impression that it could only be bought in its entirety, or even if bought piecemeal, the individual works would always be somehow connected to the installation.  Auerbach’s were as distinct art-objects as they come: almost painfully asking to be collected.

Falke Pisano The Value in Mathematics (2015) Source: Hollybush Gardens
Falke Pisano The Value in Mathematics (2015) Source: Hollybush Gardens

Having looked at two artists working with maths, I wanted to highlight the counter-example: a mathematician attuned to visual aesthetics.  Thomas Banchoff, a geometer at Brown University, pioneered the use of 3-D computer graphics to explore higher-dimensional geometries.  In the old days, mathematicians used plaster Schilling models, such as those in the Harvard, MIT, or Oxford collections, to visualise complex geometric objects.  Banchoff’s contribution was to use CGI to animate the shapes, allowing the viewer to perceive the model as it unfolds in time and thus form a mental image of what a 4-D object might look like and how it might behave.  I would argue that, by allowing manipulation of the objects, the viewer could ‘fly’ around the shape in a way that simply wasn’t possible before, and intuition could be built directly from the image, rather than being mediated through the symbolic logic of the maths, or the drudgery and expense of finding physical models.  Moreover, the physical models remain in a fixed 3-D configuration, whereas the digital allows for any 3 of the possible 4 (or higher) dimensions to be projected.

Schilling Model in Harvard’s collection of geometric models. Source: Harvard University


However, as Banchoff doesn’t reference the conventions of the Artworld, either by contextualising his images vis a vis Theory or presenting them in an arty way, perhaps he wouldn’t be thought of, nor call himself, a practicing artist [2].  Yet, I feel his works are of far greater profundity than either Auerbach’s superficial approach or Pisano’s valid and interesting, sociological critique.  They marry visual aesthetics with a potential for conceptual or perceptual access to a reality that lies beyond the mere image.

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Real and imaginary parts of the complex exponential function w=e^z. Source: Thomas Banchoff
Rotation of the Clifford Torus/Hopf Fibration in 4-D. Source: Thomas Banchoff

An artist whose approach parallels Banchoff, while acknowledging, and being acknowledged by, the Artworld, is Manfred Mohr.  Still producing, with recent shows in London (Cubitt Gallery [2015] and Carroll/Fletcher [2016/2014/2012]), he used some of the earliest plotters to produce works on paper, notably a series exploring views of the 4-D cube, a so-called hypercube or tesseract.  Mohr’s work visually has an affinity to Minimalism’s serial tradition, but genealogically is better placed in relation to Concrete Art, particularly artists such as Jeffrey Steele and Anthony Hill.  Mohr’s geometric focus, and a methodical exploration of all combinatorial alternatives, impacts the viewer through its sheer exhaustiveness and perceptual immersion.  Some of his pieces, even more than Banchoff’s, imply the physically-impossible and the infinite.  It is notable that he achieves this without colour, without any quasi-mystical or metaphysical twaddle, and his works are entirely governed by the internal logic of their generative rules.

Manfred Mohr P-231a (1978). Source: Manfred Mohr

The last, and potentially most interesting approach, is to view maths as an essentially performative practice.  ‘Performative’, a over-used word in art-speak, is utilised in a specific sense here: the act of drawing a picture, handling a plaster model, manipulating a digital model, are ways of understanding, visually and haptically, how a given mathematical concept, for instance a multi-valued complex function, behaves: where are the zeroes, where lie the saddles and branches?  This sense of the term ‘performative’ is taken up in the papers of Xin Wei Sha, a professor in Differential Topology who has sought to look at the practice of mathematics in light of analytical constructs used in art and critical theory.

In my view, what’s interesting about this approach is that it can be seen to break the understanding of a given mathematical problem into three levels: an intuitive grasp of the problem, let’s say the true knowledge; a symbolic quasi-linguistic analysis, such as a proof; and a graphical or haptic ‘feel for the thing’, which I equate with the performative.  The actual drawing, digital image, physical model, blackboard scribbled with equations are residues of a symbolic or performative method.  These physical residues can be put in a book, and indeed, if packaged a certain way and accepted as such by relevant competent judges, can be called art.  But if the primary content of mathematical understanding is fundamentally intuitive, lying somewhere between the visual, the symbolic, and the physical, then it’s likely that a non-mathematician may never really access that content.  Moreover, without facility with these tools, he/she is unlikely to communicate effectively with trained mathematicians operating in a network of peers [3].  The most we can do is ‘poke’ at it, try to access it by manipulating the geometric objects, or, more interestingly, engage in a Wittgenstinian project of ’drawing connections’ between the mathematical objects and the world-at-large.  To the extent these syntheses, these connections, are haunting and unexpected, we judge the success (or lack thereof) of art like Auerbach’s or Pisano’s.

Walter De Maria Silver Meters and Gold Meters (1976-1977). Source: Prufrock’s Dilemna blog

I end with an analogy to Land Art. Certain artists such as Walter De Maria were concerned with documenting an ungraspable moment in time and space, or in the case of his Dia Beacon pieces, an apparently obvious yet subtle mathematical idea.  Yet in the case of The Lightning Field, the primary aesthetic experience remained in him, and an element of it now invests the few viewers who can actually make it out to New Mexico.  Similarly, Hamish Fulton and Richard Long made their experience, their walks, often in the countryside, the apparent content of their work, accessible substantially to themselves.  The documentation is entirely secondary, from an aesthetic point of view, if not from a financial/re-sale perspective.  It is as if, knowing they can never compete with the immensity of nature, they made minimal, repetitive but exquisitely calculated sculptural gestures: Et in Arcadia ego.


1  Fiduccia, Joanna Report: Bullshit ! Calling Out Contemporary Art, MAP Magazine, 1 June 2010, , accessed 23/12/15.

2 See Arthur Danto’s What Art Is (2013) for an introduction to how the late Danto analysed the perennially interesting question of what art is, and the circularity in art’s definition, particularly in the age of the ready-made.

3 Subject obviously to exceptions such as M.C. Escher, and his collaboration with Lionel & Roger Penrose.

No Collars: A Sicilian Mediation

This essay was posted on the blog of the Institute of Contemporary Arts (ICA) in London, to coincide with Bloomberg New Contemporaries 2015/2016 (an annual exhibition of newly-graduated students from UK art schools, which ended 24 January 2016).  The essay accompanies a video Almadraba 38.17° N 13.24° E , and uses the colours, buildings, light and poetry of Sicily to project a multi-layered narrative.

(Im-)Migration, a topic of contemporary urgency for Sicily and Europe, as for the U.S., is given a contrasting, complementary, treatment here.  The artist, U. Kanad Chakrabarti, mines his own biography to subtly explore skilled, middle-class immigration that has contributed to American technology, medical, and academic success between the 1970s to September 11, 2001.  Moreover, Sicily itself, between 1900 and the 1960s, exported thousands of economic migrants, who contributed to the building of New York and the re-building of Northern Italy.  The artist’s treatment, perhaps, can be seen to present some light at the end of Europe’s present dark tunnel of migration.

The video’s perspective on Sicily is also informed by the island’s 12th century fusion of Arab, Byzantine and Norman culture.  As in Spanish al-Andalus, the Arab culture inflected language, food, architecture, and social norms in Sicily.  A symbol of this was the great map and atlas produced by an Islamic cartographer Ibrahim al-Idrisi.  Chakrabarti, as in previous works such as Clifford Torus (2014) or the video i j k w (2014), relates this historical world map to more abstract mathematical approaches to projection and mapping.