Mathematical Futurology: From Pseudoscience to Rigorous Framework
post by Wenitte Apiou (wenitte-apiou) · 2024-11-30T03:27:26.152Z · LW · GW · 1 commentsContents
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Futurology has long been dismissed as a pseudoscience, occupying the same intellectual space as astrology in many academic circles. This skepticism isn't entirely unwarranted - much of futurism consists of unfalsifiable predictions, trend extrapolation without theoretical foundation, and what Philip Tetlock would call "vague verbiage."
My interest in formalizing futurology isn't purely theoretical. While at Vanderbilt University's School of Engineering, I received approval for a self-designed concentration in Mathematical Futurology. The fact that an engineering school was open to such an unconventional individual study path suggested there might be merit in developing more rigorous approaches to future studies. (Though in a perhaps fitting twist for a futurist, I ended up dropping out - the irony of abandoning a traditional path while studying how institutions adapt to change isn't lost on me.)
The history of simulation-based forecasting provides interesting precedent for adding rigor to future studies. From Jay Forrester's system dynamics to modern climate models, we've seen how mathematical modeling can capture complex system behavior and generate actionable insights about possible futures. The key distinction? These approaches rely on rigorous formalization of underlying mechanisms rather than pure extrapolation.
I believe we're at an inflection point in forecasting capabilities. Modern AI developments, particularly in areas like neural ODEs, differentiable programming, and multi-agent simulation, are about to supercharge our ability to model complex systems. We're moving from simple parameter-tuned simulations to learning-based models that can discover their own parameters and even underlying mechanisms from data.
This potential for enhanced simulation capabilities led me to question: Could we develop a more rigorous foundation for futurology? Last year, I collaborated with ChatGPT to write a textbook titled "Mathematical Futurology" (an exercise in AI-augmented research itself). The goal was to build from first principles, starting with philosophical foundations:
- Epistemology: How can we know anything about future states?
- Ontology: What is the nature of future possibilities?
- Logic: How do we reason about systems that contain reasoners?
Just as Newton formalized mechanics with his laws of motion, I thought it would be interesting to propose fundamental laws for mathematical futurology. These aren't meant to be final or complete, but rather a starting point for discussion about how we might formalize the study of future states.
The Three Laws of Mathematical Futurology:
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The Law of Compounding Complexity As systems evolve, each new technological, social, or economic layer builds upon previous ones, creating exponentially more possible interaction patterns and outcomes. This can be understood through information theory - each new layer of system interaction increases the entropy of our prediction space, suggesting fundamental limits to prediction similar to how Heisenberg's uncertainty principle limits measurement.
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The Law of Adaptive Response Any significant change to a complex system triggers compensatory responses, but these responses lag behind in time and vary in proportion to both the system's resilience and the magnitude of the initial change. If we model system responses as updating on new information with some lag, we can frame this in terms of bounded rationality and delayed Bayesian updates.
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The Law of Predictive Feedback The widespread adoption of a prediction about the future alters the probability of that future occurring, creating recursive loops of influence. This relates closely to reflective decision theory and logical uncertainty. How do we reason about systems where our predictions become causal factors? This connects to work on embedded agency and Hofstadter's "strange loops."
I'm particularly interested in how these principles might inform:
- Development of better forecasting systems
- Understanding fundamental limits of prediction
- Training of AI systems to reason about long-term consequences
- Design of more robust institutions
I recognize this is a somewhat unusual approach, but I believe there's value in trying to bridge the gap between rigorous decision theory and practical futurism. I'm especially curious about:
- How might we test these principles empirically?
- What existing frameworks in decision theory and complexity science could enhance this approach?
- Could this provide useful constraints for AI alignment research?
Thoughts?
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