Non-Fungible Dimensions and the Privacy of Creativity

Before the internet, all financial transactions were executed on trading floors. Although many trades were negotiated over telephones, often the parties were each sitting on a trading floor of one variety or another. For many financial instruments all trade was required to make its way to the floor to be executed face to face. The epitome of floor trading was the futures pit. Some pits at the Chicago Board of Trade would see hundreds of traders yelling at each other and performing complicated hand gestures in a scene that looked chaotic. The average career of a pit trader could be measured in single-digit years. The stress and physicality of the job made it more like a sport. Traders, visible with bright and colourful jackets, competing verbally and physically, would conduct all trade based on the age-old honour system in which everyone knew that their “word was [their] bond.”

The story of our transition from the pits to screen-based electronic markets provides a working example of a deep principle of epistemology in action. When the new millennium rolled in, the new electronic markets sacrificed a dimension of liquidity specific to the physicality of gathering people in a single place. Despite the seeming chaos, the pit system worked. A large trader with a package to trade could execute quickly by breaking up the package and sending it to opposing corners of the pit. Forced by liquidity events, electronic markets have been the subject of authoritarian rules, but they have also evolved. Electronic markets have evolved to simulate the pits through the explicit use of privacy. This innovation exposes a relationship between privacy and the creative generation of new explanations.

Within a market there are buyers and sellers. The buyers show bids and the sellers make offers. The more willing buyers and sellers in the marketplace, the more liquid the market. Market liquidity is a measure of transactability and it is measured along two dimensions, common to both electronic and pit-based markets. The price between the best bid and the best offer is called the spread. The wider the spread the less willing buyers and sellers are to meet and transact; the tighter the spread the more liquid the market. The accumulation of all current bids and offers is called the orderbook. Sizing up the orderbook gives us the second dimension of liquidity, the market’s depth.

Trades occur within a market when the best bid and the best offer are matched at the same time and price. All trading on electronic markets occurs sequentially within a single orderbook. The pit, however, was non-sequential. In a large pit there could be many best bids and best offers. It was possible for the market to be trading at one price in one corner of the pit and another price on an opposing corner. Some traders took advantage of this by telephoning trades between the corners and capturing the arbitrage. On the surface, this seems like inefficiency. Surely transparency of price is better than the existence of arbitrage to a select group of people? This is what conventional wisdom would have us believe, but we will find that there are gains to be had from the inefficiency.

When a large trader arrives at an electronic market they are faced with a dilemma. Let’s say they have a package to sell. They can size up the depth of the bids on the orderbook, gauge the price of urgency and decide whether they are willing to pay for it. If they are not, then they may break up that package and execute it over time, but now they face uncertainty. Were the large trader to arrive at the pit, they would have the additional choice to break the package up over space: they may send the sub-packages out to different corners of the pit, where they may be executed amongst different collections of traders who are unaware of what is transpiring at the opposing corners. The pit has a third dimension of liquidity: breadth.

In an electronic market the dimensions of liquidity are visible on the screen. The spread between the best bid and offer is on display for all to see. As is the depth of all willing buyers and sellers. Despite all this transparency, a portion of the market remains private, within the minds of the participants who are yet to disclose their willingness. These sideline observers may be potential liquidity givers, but they may also be potential takers of liquidity.

The dimensions of liquidity in the pit are opaque. Imagine a trading pit as a large rectangular space, like a football field, crowded with traders. The dimensions of the rectangle do not reflect liquidity breadth or depth. And there is no single spread between the best bid and offer. We may make observations of the spread by sending out quote requests to each corner of the pit, but the spread for the pit remains opaque. Liquidity depth is similar. The depth of willing buyers and sellers within the pit remains decentralised and hidden within the minds of the participating traders.

The opaqueness of liquidity breadth, the third dimension of pit liquidity, is a transient phenomenon. When a large trader with a package to sell breaks it up and sends the sub-packages out to opposing corners, each package faces a slightly different market. Depending on the particulars for the group of traders operating in each corner, the sub-package may convey different information. In one corner, the group of traders may be net buyers and quickly consume the package. In another, they may be sellers and the package places downward pressure on the price. The balancing out between corners will take some time as information transmits its way throughout the pit. We can see that the larger the pit, the longer the time for information to disseminate and (on average) the larger the package the pit can process.

The concept of fungibility is central to understanding the nature of the pit’s third dimension of liquidity. An item is fungible when it is interchangeable with any other item of its class. A market is a mechanism for transforming one fungible item into another fungible item of a different class. All futures contracts are denominated in a currency and represent a contract for the delivery of a commodity (or financial instrument) in a specific quantity and quality. For example, the market for futures on cattle is a mechanism for transforming a basket of fungible cattle into a basket of fungible US dollars, and vice versa. We might regard the breadth of liquidity in a pit as the temporary relaxation of fungibility for either the basket of cattle or the basket of US dollars, or both. In effect, the pit consumes large orders by transforming itself into separate markets, in which fungibility between the markets is first relaxed and then slowly returns. Each separate market that occurs within the pit represents another dimension to the pit’s liquidity. Breadth, the pit’s third dimension of liquidity, is multidimensional.

Dimensionality is a core principle at the heart of good epistemology. This principle, The Principle of Dimensionality, precludes the explaining of something using itself: An explanation for a phenomenon must reside in another dimension to the phenomenon that it purports to explain. Any purported explanation that uses the phenomenon itself is an attempt at inductive inference that leads to both infinite regress and self-reference paradox.[1]

Markets produce financial explanations. Traders come to a market to transform one fungible item into another due to reasons outside of the market itself. A market’s explanatory power is measured in liquidity. When a large trader comes to an electronic market with a package to sell, they face a single dimension of buyer liquidity that is visible to all – the market depth. Should the large trader value urgency, they may execute the package immediately, soaking up the entire orderbook on display. This may induce panic. The sideline buyers resolve to wait or even transform into sellers, more selling ensues and before long the selling begets selling. This is an example of market failure where the market mechanism enters a regress. The situation is paradoxical in that some of the selling is explained only by earlier selling. These events have frequented the short history of electronic trading; they are called liquidly black holes. The pits were better equipped to handle liquidity events. They continued to provide explanatory power with their ability to generate additional dimensions.

Authoritarian solutions to electronic market liquidity events all look the same, placing boundaries on the market’s ability to process explanations. Price limits limit the price range that a market may transact in across a given trading day. During a large enough liquidity event, the market can trade only at the limit and will fail to transact at all if no trader is willing to trade against the direction of the limit. It is unclear whether the existence of such limits has a calming effect or can induces panic. What is clear is that they place a moratorium on the market mechanism – the market fails to process financial explanations.

All creative solutions to the problem of electronic markets simulate what the pit once achieved. Notice the relationship between privacy and dimensionality. Liquidity breadth in the pit was possible as the physical space facilitated temporary pockets of privacy. One electronic trading innovation simulates the pit’s third dimension of liquidity through the explicit use of privacy: A dark liquidity pool is a private exchange in which all liquidity depth and trade execution is hidden. Large traders take their business to these dark pools; and their trades are reported to the public with a time delay, or not at all. The history of dark pools extends back to 1979, when they were colloquially known as “the upstairs block market.” The upstairs market was typically responsible for 3-5% of all trading volume, however it is now thought that dark pool liquidity is as high as 40%.

The relationship between privacy and dimensionality is interesting to epistemology. All explanations are hidden from the phenomena that they purport to explain. Or as David Deutsch might quip, an explanation is a representation of “the seen in terms of the unseen.”

A problem-space depicts a phenomenon in need of explanation as a 2-dimensional abstraction – see Figure 3. All attempts at inductive inference may be thought of as attempts to use a problem-space to explain itself. The classic thought experiments confront the situation in which an inductivist attempts to infer an apparent generalisation that happens to be false – not all of Hume’s swans are white, Russell’s chicken and Taleb’s turkey will each be wrong about their continued feeding expectations. In thought experiments in which the apparent generalisation happens to be true, we see that inductive inference is nothing more than repeated observation; and when not explained these observations are better classified as problems. Problems are apparent generalisations that are unexpected or expected generalisations that just aren’t so, given our current theory. The entirety of the problem-space remains indiscernible to the problem-solver until an explanation, residing in another dimension, is discovered – see Figure 4. And when an explanation is discovered, the problem isn’t solved – a problem-space becomes discernible and the problem transforms to a dispelled generalisation (is false) or is adopted as a constant on the newly discernible problem-space (is true, but unprovable).

A true but unprovable constant can be demonstrated as follows. A pirate, who circumnavigates the Earth will not explain his predicament – that sailing in one direction always brings him back to the point of origin – through repeated circumnavigations (induction). But a creative leap into the void gives the pirate an opportunity to conjecture that his predicament as wrapped around a spherical object. The pirate’s creative leap is the act of representing the surface of the Earth, his problem-space, in terms of a third dimension. With an explanation the circumnavigation constant can be seen as true, but it remains unprovable using the surface of the Earth. We might also say that we are not privy to the explanation for the surface of the Earth from the vantage point of the surface of the Earth; the explanation maintains its own privacy.

Deutsch defines creativity as “the capacity to create new explanations.” The Principle of Dimensionality implies an alternate, though related, definition: The capacity to represent extra-dimensionally. Explanations become the artefacts of creativity. Notice too that we can bring another definition to creativity when we recast The Principle of Dimensionality in terms of privacy: the capacity to represent privately. This seems important. Our conventional depictions of creative insight see the process experienced as a flash; a lightbulb moment; a “Eureka!” The mechanisms of our very own creativity remain hidden from us, they are private.

References

Adam Tomas, “The Beginning of Infinite Regress,” Conjecture Magazine (Medium, 2020)

David Deutsch, “David Deutsch on the Infinite Reach of Knowledge,” The TED Interview, Chris Anderson (TED, 2018)

David Deutsch, The Beginning of Infinity (Penguin Books, 2011)

Dawn Arnold, My Word Is My Bond: The History of the Chicago Board of Trade (Production Craft, 2010)

“Dark Pool,” Wikipedia (Wikipedia.org)

[1] Inductive inference is the misconceived idea that knowledge can be obtained from a process of repeated observations.