Bibliography

Works on, behind, and adjacent to the mechanical view of Gaussian inference. Joshua Loftus collected many of them. His post revived the analogy.

Cotton, P. (2021). “The Analog Kalman Filter.” Geek Culture (Medium). The article this site is loosely based on: precision as mass, reduced-mass consolidation, and the Kalman filter as a limiting hierarchical model.
Loftus, J. (2020). “Least Squares as Springs.” The regression half of the story, and the direct inspiration acknowledged in the article.
Levi, M. (2009). The Mathematical Mechanic: Using Physical Reasoning to Solve Problems. Princeton University Press. A book-length case that mechanics proves theorems, springs-for-least-squares included.
Wickham, H., Navarro, D., and Pedersen, T. L. ggplot2: Elegant Graphics for Data Analysis, “A case study: drawing springs”. Hadley Wickham's worked example of rendering springs as a ggplot2 geom. How to draw these diagrams properly in R.

Pearson, K. (1901). “On Lines and Planes of Closest Fit to Systems of Points in Space.” Philosophical Magazine 2(11), 559–572. PCA, born as an orthogonal-fitting problem. The rod-on-collars of the PCA demo.
Whittaker, E. T. (1923). “On a New Method of Graduation.” Proceedings of the Edinburgh Mathematical Society 41, 63–75. The penalised smoother behind the time-series smoother demo.
Dwight, T. W. (1937). “The Fitting of Linear Regression Lines by the Method of Least Squares.” The Forestry Chronicle 13(4), 509–519. A forester fitting regressions with literal springs, ninety years ago.
Kalman, R. E. (1960). “A New Approach to Linear Filtering and Prediction Problems.” Journal of Basic Engineering 82(1), 35–45.
West, M., and Harrison, J. (1997). Bayesian Forecasting and Dynamic Models, 2nd ed. Springer. The dynamic linear model treatment in which precision coordinates are natural.
Roll, R. (1984). “A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market.” Journal of Finance 39(4), 1127–1139. The negatively autocorrelated errors of the bid-ask bounce demo.

Székely, G. J., and Rizzo, M. L. (2017). “The Energy of Data.” Annual Review of Statistics and Its Application 4, 447–479. Statistics built from a potential-energy functional of distances.
Sejdinovic, D., Sriperumbudur, B., Gretton, A., and Fukumizu, K. (2013). “Equivalence of Distance-Based and RKHS-Based Statistics in Hypothesis Testing.” Annals of Statistics 41(5). Energy distance and maximum mean discrepancy are the same thing.
LeCun, Y. Energy-based models lecture, NYU Deep Learning course. The same energy = negative log-likelihood identification, driving modern machine learning.
Grathwohl, W., et al. (2020). “Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One.” ICLR 2020.
Sohl-Dickstein, J., et al. (2015). “Deep Unsupervised Learning using Nonequilibrium Thermodynamics.” arXiv:1503.03585. Diffusion models: thermal jitter as a generative device. The dictionary's last row, industrialised.

Mount, J. (2019). “Lord Kelvin, Data Scientist.” Kelvin's tide-predicting machines: serious inference performed by pulleys and wire.
Core77 (2016). “When Splines Were Physical Objects.” Draughtsmen's splines: bent wood held by weights, minimising bending energy. Smoothing before software.
Simpson, G. (2016). “Soap Film Smoothers.” Two-dimensional smoothing as a physical minimal surface.
Strang, G. (2008). MIT OCW 18.085, Computational Science and Engineering I, Lecture 1. Spring-mass chains and their stiffness matrices. The linear algebra under every demo here.
Healy, K. Animation of least squares as springs (Cross Validated). · Goesh, T. Interactive Desmos spring regression. · Davis, J. 3D spline springs.
Friendly, M. A bibliography of physics-inspired statistical models. The wider literature, collected.

Know another Gaussian–Hookean correspondence, or a reference that belongs here? Open an issue on the springtheory repo.