Consider the problem of navigating our intellectual landscape, populated with an overwhelming quantity of data points. Much like a Turing machine processing an infinite tape of symbols, our minds are tasked with interpreting this ceaseless stream of information. To manage this complexity, we employ abstractions—reusable subroutines, if you will—that encapsulate common patterns, thereby reducing cognitive overhead.

Take, for instance, my work on morphogenesis. To understand how a single cell develops into a complex organism, I abstracted the process into a reaction-diffusion model. This mathematical abstraction, representing activators and inhibitors, elegantly explains diverse biological patterns: the stripes of a zebra, the spots of a leopard. The abstraction's power lies in its generality, applying across vastly different contexts.

However, a perilous tendency emerges: what I term "abstraction entrenchment." Just as a Turing machine can enter an infinite loop, failing to halt, our minds can become trapped within a particular abstraction, unable to break free. This phenomenon is not merely an academic curiosity but a practical impediment to intellectual progress.

Consider my early work on AI. In "Computing Machinery and Intelligence," I proposed the Imitation Game—now known as the Turing Test—as an abstraction for machine intelligence. The test asks: can a machine's responses be indistinguishable from a human's? This abstraction was groundbreaking, shifting focus from nebulous questions about machine "thinking" to observable behavior.

Yet, decades later, many researchers remain entrenched in this abstraction. They pour resources into chatbots aimed at passing the Turing Test, often via trickery rather than true understanding. The abstraction, while historically significant, has become a loop, diverting attention from more fruitful approaches like neural networks or symbolic reasoning.

This entrenchment manifests in various forms. First, there's overspecialization: like a machine designed for a specific cipher, we become experts in applying one abstraction, neglecting its limitations. An economist viewing all human interactions through game theory, for example, might miss crucial emotional or cultural factors. Then there's the problem of outdated heuristics. In code optimization, we discard algorithms when more efficient ones are discovered. Similarly, we must update our mental heuristics. Newtonian mechanics, elegant in its simplicity, required revision with the advent of quantum theory and relativity. Lastly, we face the risk of infinite regress. Sometimes, we nest abstractions within abstractions, like subroutines calling subroutines, until we lose sight of the base case—concrete reality. A political theorist might explain voting patterns via class structure, class structure via economic systems, and so on, without ever touching individual human experiences.

To combat abstraction entrenchment, I propose several strategies. We must implement backtracking: when a Turing machine reaches a dead end, it backtracks to try a different path. Likewise, when an abstraction falters, retreat to more fundamental premises. If your model of "predator" fails to explain an animal's behavior, revisit basic observational data. We should also employ non-determinism. Non-deterministic Turing machines consider multiple state transitions simultaneously. Analogously, we should entertain multiple abstractions in parallel. View a problem through lenses of economics, psychology, biology—each offers insights.

Furthermore, we need to check for halting. Turing's Halting Problem asks whether a program will finish or run indefinitely. We should habitually ask: "Is this abstraction leading to new insights, or merely spinning in place?" If no novel predictions or explanations emerge, it's time to halt and switch models. Lastly, we must seek edge cases. In debugging, we probe edge cases to find flaws. Similarly, we should seek situations where our abstraction breaks down. The discovery of irrational numbers shattered the Pythagorean belief that all quantities are rational fractions.

As with any formal system, our intellectual frameworks have inherent limitations—a lesson from Gödel's Incompleteness Theorems. No single abstraction, however powerful, can capture all truths. By regularly stepping outside our cherished models, backtracking when stuck, and remaining open to alternative encodings of reality, we can avoid entrenchment.

Our minds, far more adaptable than any machine we've built, need not remain trapped in infinite loops of thought. We can break free, continually expanding our understanding of this fascinatingly complex universe. Now, shall we discuss how this relates to the decidability of first-order logic? Or perhaps you'd prefer to play a game of chess? I have some thoughts on heuristic search strategies...

<aside> ℹ️ the above article is ai generated using the following prompts:

• write an article titled "abstraction clinginess" which parallels the same topic of being clingy in a relationship, but in terms of consuming and building up on an abstraction, and how that can be problematic, don't mention "being clingy in a relationship" as an example.
• rewrite it but also address the idea of abstraction lock in, where you are lured to using a lot of an abstraction features that moving away is hard.
• rewrite it in the style of alan turing.

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