NFTs have taken the digital world by storm, and they serve as the foundation of the emerging web3 economy. They are unique digital assets that are stored on a blockchain network, allowing for secure and transparent ownership and transfer of digital assets.
However, they are just the beginning of what the technology can offer, and as some creators have started to explore the use of Ordinal Theory to represent unique positions or ranks within a series or set of NFTs, we’re on the precipice of a new frontier. Here’s how it works and what you need to know about it.
Ordinal numbers in mathematics: a primer
In mathematics, ordinal numbers are a type of number that represents the order or position of an object in a well-ordered set. In layman’s terms, “first,” “second,” and “third” would be ordinal numbers – and the position of a point on a grid is represented by the (x,y) coordinates. A well-ordered set is a set where every non-empty subset has a lowest element, meaning that the elements in the set can be arranged in a unique and consistent order.
Ordinal numbers extend the concept of natural numbers – all positive integers from one to infinity – by representing the order or position of an object within a well-ordered set. The first ordinal number is denoted as 0, the second ordinal number as 1, the third as 2, and so on. Ordinal numbers can also be used to represent infinite sets, such as the set of all natural numbers, denoted as omega (ω).
Ordinal Theory in NFTs: possibilities and challenges
This means that the ordinal theory allows creators to make non-fungible satoshies through Bitcoin blocks – since it can be used to represent the position or rank of a digital collectible within a set or series of bitcoin blocks. This enables the creation of unique and valuable digital artifacts that represent a specific position or achievement – the same way as serial numbers would in physical trading goods – such as the first NFT minted on a blockchain, the highest-bidding NFT in an auction, or the top-ranked player in a gaming tournament.
This offers several advantages over traditional non-fungible tokens. Since they are based on the Bitcoin blockchain, they are much less susceptible to fraud and hacking. This technology also solves for the issue where the ownership proof is on the chain, but the file itself is not. Yet, ordinal NFTs remain compatible with the existing infrastructure, making them easy to use and integrate into existing applications.
From a miner perspective, there’s also a tangible monetary benefit in the form of increased fees: per Dune Analytics, bitcoin miners Generated $600,000 from ordinal transactions in just two months.
While ordinal theory offers a new way to represent unique positions or ranks within a series or set, there are technical challenges and considerations to keep in mind when creating and trading them.
Scalability remains an issue, as the Bitcoin blockchain’s capacity constraints may limit the growth and adoption of ordinal NTFs. There’s also the question of interoperability – while they are compatible with the existing Bitcoin infrastructure, they may not be with other blockchain networks, which could limit their use cases and potential applications. Ordinal NTFs also remain on a proof of work consensus system.
Most importantly, there’s the question of "OP_RETURN wars" on Bitcoin. OP_RETURN is an opcode used in bitcoin blocks to embed additional data in a transaction inside the witness side – the functionality ordinal NTFs rely on to order the tokens. This can be used to store metadata for NFTs, such as the name, description, and other attributes of digital artefacts.
However, OP_RETURN has a limited amount of space (4 megabytes) that can be used for data storage. This can lead to conflicts and competition among Bitcoin users who want to use the opcode to store their metadata. This has led to what is known as an "OP_RETURN war" on Bitcoin BC, where creators of digital artefacts compete to use the limited space available, leading to congestion and higher transaction fees.
Next, let’s take a deeper dive into the tech behind this new phenomenon.
SegWit, Taproot and the further innovations behind Ordinal NFTs
Segregated Witness, or SegWit, was introduced in 2017, greatly improving the efficiency of Bitcoin transactions by separating the transaction signature data (meaning the witness information) from the transaction data. This reduced the size of transactions and the associated fees – and in turn, greatly increased the number of possible transactions on a per-second basis from 1650 per block to 2700. This served as a significant increase of the network’s capacity while avoiding the bane of bitcoin users, the dreaded hard fork.
The Taproot upgrade, meanwhile, is a more recent innovation, fully activated as a soft fork on November 14, 2021. It provided several notable improvements like signature and transaction batching and scrambling for better privacy and more efficient use of block space, further increasing the network’s scaling potential along the way. It also came with improved functionality for smart contracts.
Combine these two upgrades, and, hey presto, now there’s a bigger witness space available to stock files and metadata.
On January 20, 2023, Casey Rodarmor, the creator of ordinals.com, tweeted this game-changer:
His new project allowed users to store any type of file – photos, videos, music, and even entire video games – in a Bitcoin transaction by linking the file to one Satoshi, with all registrations through the blocks available on his website, ordinals.com.
The SegWit and Taproot upgrades make it possible to write “inscriptions”, files directly attached to specific Satoshi. Additionally, the creation of ORD, an open-source wallet built in Rust, which has the capacity to follow the numbering of the satoshi, which is, in turn, due to the implemented general convention about the numbering of blocks based on the aforementioned ordinal theory.
Notable Ordinal NFT collections
Ordinal Punks is an exclusive collection of only 100 Bitcoin NFTs that pays homage to CryptoPunks. These NFTs were generated using a 192x192 pixel image collection through an open-source algorithm created by the pseudonymous Web3 creator FlowStay.
Currently, the lowest bid for an Ordinal Punk stands at 3.7 BTC/51.26 ETH, whereas the highest asking price for the most popular piece, Ordinal Punk 78, is 50 BTC/692.66 ETH. Recently, a buyer named Dingaling acquired seven of the Punks for 15.2 BTC/211 ETH.
Taproot Wizards is a distinctive collection of Ordinal tokens on the Bitcoin chain, created by Udi Wertheimer, an independent web3 developer. This collection comprises unique hand-drawn NFT wizards that are recorded on the Bitcoin chain, starting from Inscription 652.
The first token in the collection is notable for being the largest block and transaction in the history of Bitcoin (<774628>), weighing in at a massive 4MB. However, the project is still in its initial stages, and only a few Taproot Wizards have been inscribed on the Bitcoin chain so far.
The Wizard ID verification page on Discord only confirms six of these tokens, which include Inscriptions 1107, 1383, 2637, and 2625.
Bitcoin Rocks is a collection of NFTs that draws inspiration from one of the early Ethereum NFT collectible projects called Ether Rocks. The creator of Bitcoin Rocks, ordrocks, minted the first rock in the collection at Inscription 71, paying homage to the first rock in the Ether Rocks collection.
The collection is limited to only 100 NFTs, and some of them have been listed for as much as 1,000 BTC/13,858 ETH, which is worth over $22 million at the time of writing. The lowest bid one can make currently stands at 2.7 BTC/37.42 ETH, which is approximately $61,000.
Though there are technical limitations and challenges to consider, especially with regard to interoperability, ordinal NFTs solve many of the existing issues with non-fungible tokens and are a great way for creators to generate added value to specific entries. Their emergence is proof of the growing potential and the limitless possibilities behind the technology, and while there are still questions to be answered about their large-scale adaptation, ordinal NFTs could serve as an upgrade over their traditional counterparts.
Join the newsletter to receive the latest updates in your inbox.