A Scientific Tower of Babel

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A Scientific Tower of Babel

Jonathan Rosenblatt

The space of good ideas may be finite, while the names we give these ideas are infinite. There are many examples of redundant nomenclature. Just open the Wikipedia entry on Principal Component Analysis, to realize it was discovered and rediscovered under the names Discrete Karhunen–Loève Transform; Hotelling Transform; Proper Orthogonal Decomposition; Eckart–Young Theorem; Schmidt–Mirsky Theorem; Empirical Orthogonal Functions; Empirical Eigenfunction Decomposition; Empirical Component Analysis; Quasi-Harmonic Modes; Spectral Decomposition; Empirical Modal Analysis, and possibly more.

This terminological divergence is also found in signal processing. Here are some examples.

  1. An Electrical Engineer (EE) may say “signal detection”, a statistician may say “multivariate test”, “global test”, or “omnibus test”, and a computer scientist “anomaly detection.”
  2. A statistician will say “Hotelling’s T2 test”, an EE will say a Generalized Likelihood Ratio test, an information theoretician will say “The Kullback-Leibler divergence between two Gaussians”, and a mathematician may say “a Mahalanobis Norm”.
  3. EEs say “filter” whereas a statistician will say “nonparametric regression.”
  4. An EE and statistician may say “estimate the signal” whereas an applied mathematician will say “recover the function.”
  5. A statistician would say “discretize” or “bin”, where an EE would say “quantize.”
  6. A statistician and EE will say “predictor”, where a machine-learning computer scientist may say “hypothesis”; which is completely unrelated to a statistician’s “null hypothesis”.
  7. Anyone trained in general relativity, or differential geometry, will use the Einstein summation convention when multiplying tensors. A computer scientist may prefer to use matrix multiplications with Kroeneker products. A statistician may adhere to the Σ summation convention, even if indices accumulate.
  8. And what about those complex numbers? I can understand that they are very convenient when studying linear-time-invariant systems (i.e. convolutions), or when basebanding a signal for transmission. But why would anyone want to assume the raw measurements are complex, unless when measuring electric and magnetic charges? The EE’s affinity for complex numbers is a tremendous language barrier for statisticians and computer scientists.

Terminological divergence creates barriers. Cynicists will consider these barriers welcome: they allow us to rediscover the discovered. Most, however, will consider the unwelcome, since they impede the exchange of ideas.

There are two main approaches to eliminating communal barriers such as language: homogenize, and teach. By homogenization we refer to the idea of converging to a unified language. Klein's Encyclopedia of Mathematical Sciences served to homogenize mathematical terminology, which was diverging in the early 20’th century. This author prefers the teaching approach: where we introduce the diverging terminologies in our teaching. This will allow students and practitioners to navigate the vast realms of existing literature, and converse with colleagues in other disciplines. Much like a tradesman that trades goods between communities, we should allow practitioners to trade ideas. 



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