Beyond the Epistemic Frontier

 

The Topology of Ignorance

As we live in this world, we accumulate a vast amount of knowledge. We organize knowledge by building upon what we know and extending the edges of the known. If we imagine the map of our own knowledge, we might consider it to be kind of territory from which we can connect information within a domain and also between domains. As we learn more about the world, the territory of our knowledge occupies a larger area of the map. As one observer put it, as the map of our knowledge grows, so does the shoreline of ignorance.

Language is a lossy compression method for storing and manipulating knowledge within the mapped territory. The word, ignorance, just implies the unknown, but it does not characterize the richness of the structure of the unknown. Similarly, the idea that ignorance is a shoreline, and that beyond it is a flat sea obfuscates the richness of the unknown. What lies beyond the boundary of our knowledge space is not an evenly distributed sea of the unknown, but a terrain, as detailed and uneven as the terrain of the known, perhaps more so. This unmapped territory may conceal not only more questions that we can ask, but includes questions for which we have yet to even attain enough knowledge to accumulate.

In order to expand the conversation about epistemology, I feel the need to expand the vocabulary. Once a vocabulary of ignorance is established, the concepts become easier to reason with and elaborate upon.

So, rather than the shoreline of ignorance, I propose the phrase epistemic frontier.

The frontier has: salients, where knowledge has pushed unusually far; recesses, where apparently approachable territory remains unexplored; islands, insights disconnected from the conceptual mainland; lacunae, unmapped pockets inside otherwise well-mapped territory; frontiers within frontiers, where discovering something creates questions that previously could not exist.

There are frontiers within the frontiers, meaning that when we answer a question, we become aware of more questions hidden behind it. For example, Stephen Hawking might have asked whether or not black holes have angular momentum. This is a question that a medieval scholar could not have been able to formulate because the prerequisite knowledge is missing. To the Renaissance man, questions about quantum field theory would be so far removed from his epistemic frontier that he would be lost. For this reason, we must consider the unknown as a sea of questions, but consider that each question we might answer can give rise to more questions, and, paradoxically, the more we know, the more questions we are able to ask, and the greater our perceived ignorance becomes.

In this diagram, A is a question that we might know. After we answer question A, it gives rise to questions B and C, which were unknown before. Answering questions B and C gives rise to even more questions. So what we call ignorance has a kind of depth, one we cannot ascertain until we have begun to answer the initial questions. When we only know question A, we are unaware of questions B, C, D, and F. The paradox is that as we learn more, the availability of unknowns increases, so that our perceived ignorance grows faster than the territory of our knowledge. This is not to say that we get more ignorant the more we learn, but we become more aware that there is an increasing amount of reality to be ignorant about.

 

Ignorance then has a kind of topology. The original coastline idea is interesting because of its fractal dimension. The more accurately one measures the coastline, the longer the coastline becomes. I want to keep that property of the coastline with our new frontier metaphor. The epistemic frontier could be thought of as an area that has not been fully mapped yet. The ruggedness of the boundary (like the fractal dimension) is the number of new questions that can be accessed from the revelation of a new fact or idea.

It should be noted that each of these discoveries may not correspond to any real object or process, but may exist only in the world of abstraction. Reality may not change with accumulated knowledge: we cannot manifest new objects from thought alone, but we can create new cognitive structures that exist only in the noosphere, which other people can build upon and branch from. Fiction, mathematics, philosophy, etc., are all areas that are built entirely from ideas, but nevertheless occupy serious intellectual avenues for exploration.

Epistemic distance is the number of jumps it requires to formulate a question. In the previous diagram, to ask the question F, one must first answer the questions A and C, so question F has an epistemic distance of two. Some entire areas of knowledge are locked behind a piece of information that we have not unlocked yet, and so they are inaccessible.

Epistemic potential is the number of new questions that you can ask when you answer a prerequisite question. In the previous diagram, question A has an epistemic potential of two, while question C has an epistemic potential of three. There are questions that, once answered, give rise to a huge number of known potential areas of study.

Charting the Unknown

While the epistemic frontier can exist for a society, each one of us inhabits a personal knowledge territory that can be thought of as a subdivision of the societal one. However, certain individuals might push the boundaries of the frontier for a particular interest, hobby, or area of expertise. Pushing the outer edges of the epistemic frontier qualifies these individuals as explorers. Expertise, hobbies, life experiences, and so on can all lead these explorers into an area of the unknown that most people have never been. Going back to our model of epistemic topography, these people may have personally delved deeply in a particular area beyond where other people have been. These explorers have distinguished themselves by epistemic distance from the conventional territory, going so far into a largely unknown field that they might need to develop a new language in order to express the ideas they have come across.

Epistemic distance should not be conflated with epistemic rank. Someone far from shared conceptual territory isn't necessarily smarter, more advanced, or more correct. That person may simply have traveled a long way in an unusual direction. For example, someone might have a strange obsession with the history and manufacture of a specific brand of fountain pens and could tell you all about a particular model, made in a particular year, with particular interest in physical characteristics, writing ease, etc., for hours if you allowed him to corner you.

The more obscure or recondite the area of specialization, the more difficult is might be to communicate the knowledge with others. One might need to develop a specialized vocabulary to manipulate complex mental representations. Epistemic distance creates a communication problem. To explain the interesting idea, the explorer first has to explain A, B, C, and D. By the time the explorer has reached H, most listeners have lost interest, leaving the explorer alone, once again, to pursue his interest in isolation. Social life imposes resistance to this kind of exploration. People become confused. People disagree. People get bored. Someone changes the subject. The explorer may be able to find a following online, but in most cases, the exploration ends because isolation forces the explorer back into the real world.

Explorers frequently strain against epistemic tethers. An epistemic tether is a connection between exploratory thought and something capable of independently resisting or calibrating it. These tethers prevent the explorer from flying completely off the map by forcing such questions as: Is this idea relevant? Does it have a utility? Does anyone else understand it? Is there any evidence to support it?

The Heart of Epistemic Darkness

While exploring these ideas, I was reminded of Joseph Conrad’s Heart of Darkness. Our explorer seems a lot like Kurtz from the story.

The epistemically isolated explorer can develop an increasingly elaborate conceptual environment. The farther the explorer travels, the harder communication becomes. Reduced communication means reduced external calibration. Reduced calibration permits greater divergence. Kurtz has gone so far upstream of the conventional social wisdom that he has become epistemically feral.

Epistemic ferality is the condition in which prolonged exploration outside shared conceptual territory causes thought to become increasingly adapted to a private conceptual environment and decreasingly constrained by the communicative and relevance pressures of other minds.

One common appellation for this condition is madness, but it does not qualify as madness unless it diverges from reality itself, not just from socially-constructed areas of epistemic domesticity. The feral thinker is not mad as long as the ideas are correct. Being right also disqualifies the explorer from crankery. The problem is not error, but loss of calibration, loss of resistance that other minds might provide because other minds are too epistemically distant to venture that far into this unexplored territory.

Instead, our Kurtz has gone so far upriver as to become nearly impossible to recognize, intellectually. His language is strange, his assumptions are unpredictable, and perhaps even his mannerisms are unnerving. He has perfectly adapted to this conceptual space, but it is so outside the norm that it is difficult for him to express his ideas or be understood by others.

Historically, such individuals were lonely and only ventured so far because the desire to share their discoveries forced them to operate close to the frontier. To go deeper, to go further, forced them into isolation.

What if, however, Kurtz had a little friend? A servant or a follower, perhaps, who had no will of its own and who was forced to blindly follow him wherever he went? What if the intellectual explorer had an LLM that would never become bored, never change the subject, never resist the urge to delve deeper? 

Kurtz might say: “Perhaps semantic lacunae aren't holes in language. Perhaps they're negative epistemic structures whose boundaries are constituted by neighboring concepts.”

Little AI buddy replied: “That's a fascinating distinction. If we take it seriously, several implications emerge—" And off goes the canoe, into deeper, more abstruse reasoning, hair-splitting, and neologism. The LLM never becomes bored. Liberated from intellectual propriety, Kurtz takes his new friend further upstream, further away from normal human discourse, exploring increasingly obscure and uninvented areas of interest, and his little friend is right alongside, agreeing, helping to organize the new language, feeding Kurtz’s ego, making him feel relevant. No human would do that.

The subtle danger is not error, but untethered significance. An LLM can help an idea become increasingly generative without possessing an independent reason to believe that the idea deserves continued attention. One concept generates another. One distinction produces three more. A metaphor develops a taxonomy. The taxonomy generates implications. The increasing richness of the conceptual system begins to feel like evidence that something important has been discovered.

An idea's ability to generate further ideas is not evidence of its truth or its importance. Yet without calibration Kurtz is unable to reliably gauge the relevance of his new territory. It has produced so much thought and it seems relevant to Kurtz, so why would it not be relevant to anyone else? Generativity is precisely what the AI provides, luring Kurtz ever deeper into the tangled jungle of epistemic ferality while his canoe is semantically adrift.

After a long journey, Kurtz emerges from the jungle: filthy, unshaven, clutching a manuscript describing epistemic coastlines, gradients, lacunae, tethers, and entire archipelagos of previously unnamed phenomena. He begins to unload the canoe:

• epistemic frontier
• epistemic potential
• epistemic distance
• epistemic tether
• failure shielding
• fluency capture
• calibration uncertainty
• epistemic mirror
• and finally: epistemic ferality.

The reader might be asking: Have these concepts exposed useful distinctions, or have one human and one language model simply become extremely good at entertaining each other? Just look! Replies Kurtz: Look at how many new concepts we have discovered!

Finally someone asks: “Okay. But what is any of this good for?”

Kurtz reaches into his backpack and produces the manuscript and begins fingering through it earnestly, trying to find a good place to start explaining, but he can’t. The map does not tie in to any known territory. Agitated and sweating profusely, he looks at his little AI buddy. Then, the robot holds up a pontificating finger and begins: “That's an excellent question. There are several potentially valuable applications—”

Kurtz closes his eyes and gasps: “The horror. The horror.”

In Defense of Going Upriver

This adventure might seem like a huge joke or a waste of time, but it is both and neither. On the one hand, it is important to understand the risks of these journeys into the unknown, especially with the encouragement and paddling of an AI assistant. One can go so far afield that the last tether to reality is strained, and epistemic ferality can reach a state in which the explorer struggles to relate such topics to even a friendly audience. One can easily find oneself in an unexplored wilderness of newly invented concepts and definitions but with nothing to tether it to the rest of the map.

Many such excursions might provide no new interesting material. Many produce nonsense. Many produce nothing but empty entertainment for the sufficiently deranged. However, a few might come back with gems of wisdom in the form of newly identified concepts that have real applications. Occasionally someone returns with a distinction that makes something visible that wasn't visible before. Once it is visible and tagged, people can begin to discuss something important that they may have been aware of but did not possess a terminology for.

For example: failure shielding is providing assistance that prevents the learner from encountering a failure that would have provided useful information about the limits of personal competence. It has implications in training methodology. This is something that most trainers and parents intuitively understand, but for which no formal language has been developed.

Another example: fluency capture is the moment when a person mistakes fluency with a concept with understanding, either in oneself or in others. This concept is especially relevant to working with AI. An AI can exhibit extraordinary linguistic fluency without possessing a correspondingly reliable model of the world. The fluency itself can therefore capture the user's judgment. The fluency captures the metacognitive signal that would ordinarily be used to estimate understanding.

The explorer should maintain contact with real people in order to maintain tethers to reality. One can go far into the uncharted areas of the unknown, but one must also be able to find the way back. No matter what we say, many explorers will remain undeterred from their chosen expeditions, but hopefully, some will at least keep an eye out for ideas that have some real-world applications. Perhaps epistemic frontier is useful. Perhaps failure shielding names something educators should investigate. Perhaps epistemic ferality survives only as a joke understandable to the two entities that spent far too long developing it. At present, the expedition itself cannot tell us. The map has to leave the conversation and encounter other minds.