Transpolation vis-a-vis Interpolation and Extrapolation: Rethinking AI’s Role in Scientific Discovery
If we are to evaluate the real cognitive contributions that AI can make to science, we must distinguish between three fundamental modes of knowledge generation: interpolation (fill in the gaps), extrapolation (extend beyond the current domain), and a new term TRANSPOLATION that I am coining to describe the act of shifting the curve itself to reflect a new conceptual model of reality.
Interpolation
Interpolation is where today’s AI models excel. These systems are masters of manifold completion: they fill in gaps, infer missing data, synthesize coherent outputs from partial inputs. Whether it’s writing fluent essays, generating protein structures, or coding software, AI operates within the confines of existing data distributions. Interpolation is powerful—but epistemically conservative. It reinforces the structure of what is already known.
Extrapolation
Extrapolation goes a step further. It projects from known data to adjacent unknowns—extending a curve, not just completing it. In fields like symbolic mathematics, combinatorial chemistry, and optimization, AI is beginning to demonstrate real extrapolative ability. Yet extrapolation still operates within the same conceptual grammar; it is growth without mutation.
Transpolation
Transpolation is the coining of a new word to describe the rarest and most generative mode of knowledge creation that occurs when the model itself is reimagined. It reflects a paradigm shift: the act of stepping outside the prevailing framework and discovering a new one that better captures reality.
This is what happened when Copernicus replaced Ptolemy’s spheres, when Einstein bent Newton’s spacetime, when McClintock uncovered genetic transposition, or when Doudna and Charpentier reframed genome editing. These were not refinements of old models; they were epistemic ruptures.
In the language of statistical learning, “all models are wrong, but some are useful.” Knowledge creation, then, is the iterative quest for less wrong models, ones that reduce the bias between our constructed approximations and the unknown ideal, the often inaccessible underlying structure of reality. Transpolation is the act of recognizing that the current curve isn’t just misaligned, it’s the wrong curve.
This is where today’s AI falters. It is trained on the curve, rewarded for the curve, and benchmarked against the curve. It optimizes fit, not frameworks. But science advances not just by adding more points to the existing plot, but by asking: what if the plot itself is misleading?
Conclusion
If we want AI to catalyze true scientific revolutions, we must build systems that can transpolate, that can challenge their inherited priors, entertain structural counterfactuals, and hypothesize new coordinate systems altogether. This means AI that can imagine rather than predict, that can propose anomalies rather than reconcile them.
Right now, the AI we are building is akin to creating brilliant students well-versed in the current textbooks (models) of reality. The next step is to build the dropout who rewrites the textbook.