Art Crypto Projects

Certificate of Inauthenticity

“Certificate of Inauthenticity”, 2020, ERC-721 Tokens.

Provably inauthentic art.

A follow-up to my collaboration with Furtherfield.

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Aesthetics Crypto

Aesthetic Comparison Games

Using ideas from design theory, provable computation, and calculus we can construct games of aesthetic comparison with arbitrary precision. These games can be represented in a form that allows them to be resolved using blockchain smart contracts via reference to materials submitted to set up the game, by reference to on-chain precedent, or as a last resort by appeal to a third party oracle.

Game Setup

To construct the game, two parties must agree on two images, on the properties of the elements of those images under consideration, the relationship between them that is under consideration, and the degree of that relationship.

▲ = ▲ ?

The properties must be represented electronically and atomically, for example as RGB colours, as extremely small pixmaps, or as simplified bezier curves. The hashes of these values are then arranged as the leaves of a merkle tree for each image, in lexicographic value. A third three is then constructed by the first party of the hashes of tuples of pairs of leaves from each of the first two trees, the name of the relationships that is held to be true between them, a stated tolerance for deviation from simple mathematical equality in that relationship, and the weight of these properties as evidence in the aesthetic assertion being made accorded to that relationship (this must sum to 1.0 for all leaves). A threshold for property significance is declared (e.g. 0.001), this may be updated in later rounds of the game with mutual agreement or by appeal.

These trees are then combined with the root of two further trees – the precedent tree and the adjudicator address tree – to produce the merkle root of the game setup. It is vitally important that both parties agree on the representation of each image contained in the tree and on the tolerances and weights accorded to elements from them. It is trivial to make green into red with a high enough tolerance for colour difference, for example. Tools to automate preflight tests for game trees will be important.

For a multi-stage merkle tree acceptance phase, use rounds of committing/revealing proposed trees with increasing stakes. Accepting a tree returns the stakes. There may be a time or round limit for this phase, or no hard limits on agreement only exit rules.

Compulsory/voluntary comparison games may require different agreement, comparison and appeal phases to avoid griefing. Or a single well-understood workflow with well-understood and clearly described failure modes in each contect may be easier to reason about and therefore ultimately more reliable.

Game Rounds

Once the game root has been registered, the comparison proceeds in rounds of assertions made with reference to the content of the subtrees that the root anchors.

If the comparison can be made automatically (e.g. #FF0000 == #FF0000), this proof can be offered onchain. An uncontested assertion of this form wins.

Example comparison relations and properties include: =, ≠, ≈, ≉, ⊂, ⊄, ⊃, ⊅, <, >, geometric affine transform, colour difference, freeform textual statement.

Beware of image content when comparing. Steganographic information may mislead automated comparison.

Where statements can be phrased equivalently, the one that would place the lowest value on the left branch should be used.

Unrealistic trees, e.g.

 / \
◯   ▧

can be rejected by submitting a contradictory precedent or an appeal if evaluation is binding, can be replaced with a more accurate proposal in a multi-stage MAST acceptance opening phase for a comparison game, or simply not entered in to if an evaluation is not binding.

If comparisons can be reduced to precedents, cite them. This means that if a comparison has been resolved in a previously successfully completed comparison, submit the merkle path of that proof and the merkle path of the properties that it matches in the properties tree instead of starting an appeal. An uncontested assertion of this form wins.

If either party wishes to reject an assertion they can provide the merkle path to a contradictory assertion.


If the content of the game tree root is exhausted by assertions without a simple winner emerging, either player may attempt to establish a new prededent by assembling a pair of merkle paths from the property trees of the attacker and the defender, staking a pre-agreed amount of value that will be forfeited if they lose the appeal, and sending the appeal to a third party tribunal implemented using prediction markets, an ombudsman oracle DAO, or some other means.

The outcome of the appeal becomes available as a precedent for future games.

Game Outcome

Ultimately a winner will emerge, in which case they can exercise the right granted to them by a pre-game commitment to update a DAO’s state or receive an amount of cryptocurency or some other action that a proof of resolution can enable. Or both parties can co-operate to declare a winner or a draw before that, either returning any stakes, burning any commitments, or co-operating to exercise the commitment that the winner would have been able to exploit.

Aesthetics Art Crypto

Intensive and Extensive Aesthetic Property Token Composition

ERC-721 tokens can be composed into tree structures using ERC-998 tokens. Where those ERC-721 tokens represent images or image elements, that tree structure becomes a rendering tree or two-dimensional scene graph (three-dimensional scene graphs will have to wait for 3D Rare Art standards to solidify). To lay out the elements of the image we must be able to transform them in various ways, changing their position, size, colour and other intensive and extensive aesthetic properties. We can represent these aesthetic properties as ERC-20 tokens with 18 digits of precision as they are continuous quantities.

To apply these properties to an ERC-721 token we can attach them using an ERC-998 composable tokens in an SVG-style tree hierarchy. Each ERC-998 token has one or more quantities of ERC-20 aesthetic property tokens attached, one or more child ERC-998 tokens, and zero or more (usually zero or one) ERC-721 tokens attached. The properties expressed by the ERC-20 tokens attached to each ERC-998 token are applied to any attached ERC-721 token(s) and transitively to the children of any attached ERC-998 tokens.

Where the values we wish to represent should be limited to a given range (e.g. 0.0 .. 1.0 or 0 .. 255), we can either assert if too many tokens are are sent to be attached to ERC-998 tokens (we might also be able to refund them in an additional transaction, but this would affect the gas required – and as per the ERC-20 standard we should not accept fewer tokens than are sent), we can treat higher values as meaning the maximum (e.g. 3.1 is 1.0, and 1337 is 255), or we can scale values relative to the largest quantity.

When the values must be both positive and negative (for example if we are representing co-ordinates around an origin, especially relative co-ordinates in a group hierarchy), we can use a second token to represent negative values (this would be better represented using ERC-1155 tokens but ERC-998 does not support this standard). If both positive and negative tokens are applied their values should be summed. For co-ordinates we can use only positive tokens by treating group origins as their top left rather than their centre and only adding positive offsets to child ERC-998 tokens.

Affine transformation ERC-20 tokens are applied as a transformation matrix to the children of the ERC-998 token they are attached to. This means that children-of-children multiply their parent matrix with their own. There is an implicit graphics state push/pop for each ERC-998 token, so transformations do not affect sibling tokens, only child ones.

For colour or alpha (transparency) values, these values are added to the colour values of the image represented by the token. This may not be the expected behaviour. As with co-ordinates, using only positive values can be achieved by carefully structuring the hierarchy of the image so that child ERC-998s only need to add rather than subtract colour values to represent their colour scheme. Alternatively we can treat colour tokens as scale, allowing both increases and decreases of colour to be expressed across the token hierarchy, and source primitive forms to be arbitrarily coloured if they are white. More complex colour interactions and other filter or layer behaviours could be specified by additional tokens.

This gives us the following ERC-20 tokens:

X x co-ordinate offset values in distance units.
Y y co-ordinate offset values in distance units.
WIDTH width in distance units.
HEIGHT height in distance units.
ROTATION rotation in degrees.
Unbounded, wraps around past 360 as usual.
RED red scale.
Unbounded, although values that multiply the source value higher than 1.0 will have no additional effect.
GREEN green scale.
Unbounded, although values that multiply the source value higher than 1.0 will have no additional effect.
BLUE blue scale.
Unbounded, although values that multiply the source value higher than 1.0 will have no additional effect.
ALPHA transparency scale.
Unbounded, although values that multiply the source value higher than 1.0 will have no additional effect.

What is to stop the owner of an artwork created in this way from breaking it up, re-arranging it, or adding to it?

Nothing at all…

Isn’t this an extremely expensive way of assembling art on-chain?

It depends on the value of the work that is made using it…

Art Art History Artificial Intelligence Crypto Philosophy

AI Art, Ownership, Blockchain

Questions of “ownership” in art can be a matter of law, of social norms, or of art theory. New art forms and new methods of producing art can fall foul of existing answers to these questions or creatively re-open them. Often they do both. “AI Art” produced using contemporary “Artificial Intelligence” artificial neural network software is a good example of this. “Rare Art” produced using blockchain token software is another, which we will consider below in relation to one particularly notorious example of AI Art.

“Portrait of Edmond Belamy” was produced by the artist group “Obvious” using an existing artificial neural network model trained on a corpus of images of classical paintings. Obvious did not credit the author of that network model, or any of the artists whose paintings were included in the corpus. At this point there are already three different layers of questions around ownership.

Firstly, the assembly of an image corpus. Accurate reproductions of paintings that are no longer in copyright should not attract copyright, and in the US at least this is quite rightly the case. A collection of such reproductions may attract copyright on the collection itself, but this should not affect individual works within the collection. If the images were of paintings that are still under copyright, copying each image might infringe that copyright. I say “might” because doing so might fall under fair use/fair dealing (hereafter just “fair use”) exceptions to copyright. These exceptions are popular both with artists who work with appropriation and with large Internet companies who work with search and advertising. Both groups, and others such as Digital Humanities scholars, might wish to assemble such corpora of images so it is difficult to generalise about motives and outcomes regarding them. In the case of art, however, fair use for artists is a key defence of artistic creativity in an age where the visual environment is dominated by corporate media.

Beyond this legal view is the ethical and art theoretic view. Is it right to treat individual artworks in a corpus as tokens of a type or as just part of a set, as fodder or as raw material for an industrial process? With apologies to Clement Greenberg, does discarding the tactile elements of painting still meaningfully capture it, and does discarding visual detail and differences in scale discard more for processes of derivation than processes of study?

Secondly, the training and use of the artificial neural network model on that image corpus. The model is trained by processing images in the corpus, by copying and reading their data. The model will contain representations of parts of the images from its training corpus, and its output will also resemble parts of the images they are trained on. Mechanical copying and creating derivatives of images are covered by copyright. Cutting up images and juxtaposing them with the work of other artists is covered by the moral rights that accompany copyright. Again, copyright does not apply to works that are out of copyright (moral rights vary by country…), and artists should have a claim to fair use of such materials. The degree to which artistic use of source materials transforms them should be a factor in establishing that such use is indeed fair use, and the output of artificial neural networks certainly transforms the images that they are trained on. Style is not copyrightable (let’s not talk about “trade dress” here), but forgery and “passing off” can be legal matters, and the application an artist’s signature style to a work that they have not made but is sold under there name is the same whether performed by human hand or algorithm.

Again, the ethical and art theoretic view raises more questions. Signature styles are a matter of pride as well as profit for artists, and while this can be critiqued within art theory it is a strongly established norm that simple imitation of style, without a critical framework for doing so, is a breach of artistic norms. Artificial neural network models need not operationalise an individual artist’s signature style in order to devalue the concept of signature styles in general.

Thirdly, Obvious’s use of existing neural network software to generate an image has caused widespread debate. “Signing” the image with the algorithm used by the artificial neural network software to produce it functions as a double-bluff whatever the intention behind doing so. We know that Obvious produced and sold the image, their attribution is not threatened by this. But it erases the work of both Robbi Barret in producing the model of art that the image is simply a product of and of the artists that the neural network’s model already erases the authorship of, both in terms of attribution and in terms of control of their work (even if from beyond the grave in the case of the corpus artists). Software authors should not be able to control uses of the tools that they produce – Microsoft should not be able to censor your writing using Word or claim joint authorship of everything you write using it. But a trained artificial neural network model is a more complex thing than a text editor from this point of view – it is as much content as it is tool. Microsoft should not be able to tell you how you change the contents of an empty text document, but changing a novel or a painting whether represented physically or digitally may infringe on the copyright and moral rights that it may have. Again fair use should be strongly considered for artistically transformative use of artificial neural network models.

Art theroretically, such direct and uncredited use of existing materials, even materials created by another artist, may count as appropriation art, which is an established category within the arts. Appropriation art is deliberately transgressive, often for critical effect. Appropriating non-art or low-art materials is very different from appropriating canonical art or the art of leading contemporaries but both can be critical moves. Artistic labour can be appropriated directly, in the case of contemporary artists who use studio assistants to produce art under their own signature such as Jeff Koons or Damien Hirst. The signature that the products of this labour are exhibited and sold under is a key part of its erasure. And where software used to make art is free software(/open source), attribution may or may not be a strong social norm but past a certain point that attribution is useful information to have for artistic, critical, and art historical engagement with the work.

Prior to this, Obvious had already encountered the question of ownership and found an answer that led directly to “Portrait of Edmond Belamy” being sold at auction. That answer was based on AI’s twin in contemporary technological hype, the blockchain.

Christie’s discovered Obvious via their work on Superrare, a blockchain-based “Rare Art” platform. Rare Art is named after the “Rare Pepe” project that developed the techniques of using cryptocurrency and blockchain token technology to record limited edition certificates for digital images. This produces “artificial scarcity” and allows a form of ownership for pieces of digital art art that would otherwise be infinitely reproducible. This use of certificates as ownership proxies for art was pioneered by conceptual art. Compared to a flammable piece of paper with a handwritten signature on, the authenticity of a blockchain transaction secured by a not inconsiderable fraction of the world’s computing power each day only increases over time. It may not be entirely clear what the authenticity is of, but the terms and conditions of Rare Art platforms and the community norms of their users and consumers do produce a vivid image of a novel and very strong concept of ownership.

“True digital ownership” on a blockchain secured by cryptographic keys is seen by its proponents as stronger, more trustworthy, and more absolute than previous conceptions of property. This makes AI art a natural fit for Rare Art because each has needs that the other fulfills: ownership in the case of the products of AI art, strongly perceptible uniqueness but also recognisability as art in the case of Rare Art. Sale at auction also provides this kind of closure for the financial value of art, but new art and in particular digital art faces a bootstrapping problem in which it must establish its value in order to be sold at auction but cannot be sold at auction without first establishing its value. Christie’s saw art by Obvious selling on Superrare and could react to that market signal more quickly and with lower risk than with signals from gallery or online sales of physical goods.

It is a truism of International Art English that art questions things. There are many questions in play in both AI Art and Rare Art. They involve the concept of ownership considered in terms of the law, of social norms, and of art theory. The answers to these questions from within each of these realms individually may be obvious and simple to their practitioners, but between them they may be more at odds than each realises. Negotiating this without closing the door to cultural creativity or opening it to corporate exploitation is a task that is of interest far beyond the artworld.

(I am not a lawyer, etc.)


Oracles Are The Oracle Problem

In computer science, an “oracle” is a source of truth from outside the system. On a blockchain, this means that oracles provide information that is not part of the transaction protocol. This can be the price of the US dollar, the weather in a particular location, whether a particular celebrity is still alive, or other facts that are not simply protocol-level transfers of coins secured by cryptographic signatures.

The introduction of truth that cannot be enforced at the protocol level or checked entirely by reference to the prior history of the blockchain means that oracles introduce a question of trust. Like the economic trusted third parties that Satoshi Nakamoto sought to exclude from the original Bitcoin protocol – who are better understood as treacherous third parties (to channel Richard Stallman’s critique of DRM for a moment) – oracles introduce trusted third parties for knowledge. Since demand for the information that oracles provide is ultimately economic, this amounts to the reintroduction of economic trusted third parties.

Various mechanisms can be used to address the risk of trust in oracles. Reputation on- or off-chain, or economic incentives enforced using different rewards and punishments, for individual providers or communities or markets providing information. Each scheme has its failure modes, and each ultimately requires trust in the behaviour of off-chain participants to act in an economically rational manner.

Oracles are unavoidable for a large class of problems but where they can be creatively avoided it is worth exploring alternatives. The use of token trade volumes and prices over time in DeFi applications to establish interest rates is a good example of this. Where on-chain facts cannot be tautologies, if they can be inferred from other on-chain facts this will be more robust than oracles if those facts cannot easily be manipulated. Ideally this means protocol-level facts, or at least facts with robust on-chain incentives for truthfulness.

Given this, “the oracle problem” is not how best to implement trusted oracles. It is the existence of oracles. Let’s continue to find creative ways to extract off-chain information from on-chain truth.

Crypto Philosophy

Why Bitcoin is Money According To Marx

tl;dr: whales.

In “Marx on Money“, Suzanne de Brunhoff describes the theory of money that Karl Marx presents in “Capital”.

Money, for Marx, emerges in three stages prior to capitalism.

In the first stage, gold becomes a measure of the value of all other commodities rather than simply one commodity among many.

In the second stage, gold coins become the medium of circulation. Once gold becomes de-materialized in this way its role can then be occupied by fiat currency.

In the third and final stage, the emergence of hoarding paradoxically introduces money “proper”.

de Brunhoff writes that “Hoarding is a demand for money as money…”, an interruption in the circulation of money that “…serves to ceaselessly preserve and reconstitute the money form as such, whatever the deformations, transformations, and disappearances it undergoes as a result of the other two functions. Produced by these, it becomes in its turn a condition of their functioning.”

In the crypto space, hoarders are known as whales. They remove their coins from circulation with the expectation that this will ultimately provide them with more utility than immediately spending them. In this they act just like hoarders of gold coin or fiat currency. To quote Marx, “The money becomes petrified into a hoard, and the seller becomes a hoarder of money.”

Whales therefore establish that cryptocurrency is money according to Karl Marx.


Staking Planes

=========o========= – Art
=========/========= – Media
========oo========= – Sensate
=========o========= – Geodata

Stake conceptual dimension as well as spatial position.

Build on lower level stakes (…assertions). Sensates must be placed on geodata, media and art above that.

Lose stake to challenger if your assertion is bumped to another plane (including the Plane of Falsity).

Appeal to Aesthetic Comparison Games, or use pure stake?

Crypto Magick

Entirely Unsatisfactory Notes Towards An Imagined Cypherpaganism

The book of nature is encrypted.

Encryption is the production of nature.

Ciphers are deiforms.

De/ciphering is ritual.

Ontology is mathematics.

Universes are sets of objects.

Cryptographic spaces are universes.

Occultation is placing out of sight.

To en-crypt is to place in a crypt.

Events are trapdoors.

Nature loves to conceal herself.

Alice, Bob and Carol are archetypes.

If nature is unjust change nature.

What if nature isn’t natural?


glTF ERC-721 NFTs

What is it?

3D rare digital art made by minting ERC-721 NFT tokens that represent 3D models rather than 2D images.

(Building on by simplifying the approach.)

How does it work?

Add a “model” field to the metadata for an NFT that is a uri pointing to a .gltf model, using only standard (non-extension) glTF features.

Then allow these models to be placed in blockchain virtual worlds. The in-world position of placing the entity representing the token for that model is the origin at which that model is rendered inline.

VR World platforms should enforce that if the owner of a parcel of land or an avatar wishes to attach the model represented by the ERC-721 token they must own, via the same address, both the item that the model will be attached to and the model that will be attached to it.

If you are concerned that this allows the owner of a token to use the same item in different virtual worlds then use an ownership proxy or extend the contract to register its current “location”. But we don’t worry about that for image art NFTs, not yet at least, so I suggest waiting to see if anyone really cares about this for 3D art NFTs.

Why glTF?

It’s a modern standard with reasonable features that is well-supported by the kind of web technologies used to make blockchain virtual worlds.

How do I implement this?

Add the following field to the ERC721 Metadata JSON at the uri returned by tokenURI() for the token:

"model": {
  "type": "string",
  "description": "A URI pointing to a resource with mime type model/* representing the asset to which this NFT represents."

Then set it to a .gltf file.

For the image field of the file, either include an image preview of the model or use the glTF logo. When the image is the glFT logo, a preview must be created from the model file. How can you tell if the image is the glTF logo? If the filename is gltf.(png|svg|jpg), it’s the glTF logo.

But what about…?

Do not worry about anything else.

The token metadata should not include a bounding box, because that can be calculated from the model file and could be incorrectly specified.

Voxel vs. mesh vs. primitive vs. metaball virtual worlds should all inline the same model, and there should be one model per glTF file. That model’s aesthetic is more important than the world’s, that’s part of true digital ownership. If a virtual world wants to voxelize or LOD it, that’s the world’s problem.

Support for proprietary or single-world formats should be frowned on but someone is going to try to embrace, extend and extinguish this at some point. Just ignore them, we don’t need to legislate against that here.

Aesthetics Art Crypto

Tokenized Vickrey Aesthetics

In “Radical Markets”, Eric Posner and Glen Weyl propose a system of universal, permanent second-price “Vickrey Auctions” of land as a mechanism for price discovery on the utility of property and the taxation of the ongoing ownership of that value with a “Harberger Tax” as the means of funding a just, redistributive, state. They call this the “Vickrey Commons”.

Critics of the Vickrey Commons proposal tend to focus on the fact that everywhere is always for sale to the highest bidder rather than the fact that the accompanying tax is intended to ensure socially productive use of property and to securely fund social welfare. From a cypherpunk or cryptocurrency point of view however, the intrusion of the state into property relations is inherently unjust and distortive of social relations. We will return to the redistributive element of the Vickrey Commons later, but for the moment it is its capacity for driving price discovery and productive use that I wish to focus on.

Vickrey Auctions are often used by states to privatise radio frequencies in the electromagnetic spectrum. Extending this to the visible spectrum, to colour, would be the stuff of satire. But below the state level we do see the inefficient allocation and exploitation of colour and other aesthetic properties in the artworld. We can tackle this using the intelligence of markets and simulated property rights on the blockchain.

Let us first make individual colours, shapes, line and surface qualities and other aesthetic properties representable as non-fungible tokens on the blockchain. These can then be sold. The right to use those properties can then be sold by the owners as fungible tokens.

Compositions of these tokens can then be represented in turn by a secondary layer of non-fungible tokens and usage rights for those expressed by their own higher layer of non-fungible tokens.

This process can be repeated until concrete instances of the expression of asthetic properties are expressed by composing non-fungible tokens from different layers into a non-fungible token that can be treated as unique or, alternatively, editioned using a final layer of fungible tokens.

If we use the Ethereum blockchain for this, the system can be represented as a stack of ERC-721, ERC-1633, ERC-20, and ERC-998 smart contracts.

In the absence of rent or taxes, the owners of non-fungible aesthetic properties can make money by selling those tokens or by releasing and/or re-purchasing fungible tokens that represent them. The optimal strategies for this are outside the scope of this essay, but do involve reacting to demand at different levels for fundamental and derived/composed properties in a timely manner.

Returning to the redistributive aspect of the Vickrey Commons, we can (pre-)sell the fundamental aesthetic properties to one or more foundations that exist to profit from them in order to redisttibute those profits to deserving artistic and/or social causes. It is possible to imagine various ways of structuring those foundations as smart contracts or their payment(s) as domain-specific tokens, although introducing a Tokenized Aesthetic Vickrey Commons currency coin risks the introduction of a central bank-like entity into the system.

Where the foundations’ revenue must go to the authors of works using those properties, this is possible to enforce simply on-chain although avoiding the sybil problem and other issues with on-chain redistribution is much less simple. Where we wish to enforce more complex relations between the work and the foundation we will need aesthetic comparison games, which can be completed onchain but are much more expensive than a simple token check. Where the foundations’ missions are more arbitrary, controls begin to look more like human organization than enforcement through code.

It is not possible to exclude duplicate token contracts on a given blockchain without support for doing so at the protocol level, and in the general case it is impossible across blockchains without protocol support for a cross-chain proof-of-precedence protocol. It is even easier to simply not use these tokens. Why, then would anyone use them?

Anchoring a singular source of these properties through first-mover and network effects may be sufficient to make it authoritative for anyone who wishes to use them. The use of these tokens is then a means of establishing price and authenticity, which if we squint hard is to say it is a means to establish value.

Further objections to this translate neatly into objections to the artworld and schemes to reform or replace it.