Lotka's Inverse Square Law of Scientific Productivity: Its Methods and Statistics

Stephen J. Bensman; Lawrence J. Smolinsky

Home/Archive/arXiv

arXiv · 1601.04950

Lotka's Inverse Square Law of Scientific Productivity: Its Methods and Statistics

Stephen J. Bensman·Lawrence J. Smolinsky

View original source ↗Read source document ↗Export metadata ↓

Abstract

This brief communication analyzes the statistics and methods Lotka used to derive his inverse square law of scientific productivity from the standpoint of modern theory. It finds that he violated the norms of this theory by extremely truncating his data on the right. It also proves that Lotka himself played an important role in establishing the commonly used method of identifying power-law behavior by the R^2 fit to a regression line on a log-log plot that modern theory considers unreliable by basing the derivation of his law on this very method.

Explore related subjects

cs.DL

Keep this discovery

BibTeX RIS

Stephen J. Bensman, Lawrence J. Smolinsky. 2016-01-19. Lotka's Inverse Square Law of Scientific Productivity: Its Methods and Statistics. https://arxiv.org/abs/1601.04950

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

INDRA: A New AI Tool for Exploring Tobacco, Fossil Fuel, and Chemical Industry Archives

Five decades of litigation have disgorged hundreds of millions of pages of formerly secret business records from the tobacco industry, along with documents from the makers of drugs, chemicals, food, firearms, and fossil fuels. Yet these archives have been effectively inaccessible to general-purpose large language models (LLMs) because they have never been compiled into an LLM-readable corpus. Chatbots may be familiar with some of the materials contained in such archives but, with no direct access to the documents, they are vulnerable to hallucination and other defects. Here we introduce INDRA, a research platform designed to remedy such failures by embedding the conventions of archival historiography into a system-level protocol governing every output. The platform federates UCSF's Industry Documents Library, Columbia and CUNY's ToxicDocs, Stanford's SRITA, and other heretofore siloed collections, and provides three interlinked safeguards: (1) a closed evidentiary sandbox confines the model to a user-selected corpus, blocking retrieval from external sources that could introduce bias; (2) real-time provenance tagging marks the boundary between archival evidence and parametric inference; and (3) a system-level protocol enforced by deterministic scripts guides the structure of every output. Together these safeguards prevent the model from conflating "the documents say X" with "I think X" or "I learned X from prior training." The result is an LLM-powered research partner enabling massive multi-archival investigations, a tool whose outputs are designed to be checked rather than trusted, and whose architecture makes the conditions of knowledge production visible and auditable. Three case studies demonstrate the method's analytical value and limitations, including what we call the Heraclitus effect, the steppingstone dilemma, and the gullibility (or mafia) problem.

cs.DL↗

arXiv2026

Wavering Oracles: Selective Updating and Correlated Failures in LLMs and Their Implications for Scientific Workflows

Scientific workflows increasingly use repeated queries, multiple models, and interacting agents. Reliability therefore depends on whether models preserve correct conclusions, accept valid corrections, and contribute errors that a selector can distinguish. Using SycoBench- 600 as a controlled measurement substrate, we evaluate these requirements through selective updating, defined by resistance to misleading suggestions and uptake of correct suggestions. The study covers ten models and 17,055 trajectories. Published models span 13.4 to 71.6 percentage points in selectivity. Under identical local evaluation, Qwen3-4B is selectively adaptive at 45.6 points, Gemma3-4B is destabilized at minus 14.1 points, and SmolLM3-3B follows both correct and wrong explicit suggestions, producing zero selectivity. Matched interventions identify model specific responses to doubt, authority, and explicit advice. Among seven published models, the best reaches 95.3 percent accuracy, plurality reaches 88.6 percent, and the oracle ceiling is 99.8 percent. Mean error correlation of 0.285 reduces seven models to an effective independent count of 2.58. A leave-one-stem-family-out reliability selector reaches 96.2 percent, recovering 67.7 percent of the plurality-to-oracle gap. These results establish selective updating, error diversity, and calibrated adjudication as jointly measurable design targets for multi-model scientific workflows.

cs.DL↗

arXiv2026

Same Problem, Different Field: Cross-Domain Solution Import via Domain-Stripped Computational Fingerprints

The same underlying computational problem is solved across unrelated fields under different names: recursive Bayesian state estimation appears as a "Kalman filter" in control, "Bayesian forecasting" in pharmacokinetics, and "data assimilation" in geoscience. Topical and citation-based scientific embeddings cannot see this shared problem. We distill each paper once into a domain- and method-name-stripped faceted computational fingerprint, a free-text mechanism skeleton plus controlled computational facets. We define a tunable, facet-selectable distance over it. The goal is solution import: surface cross-field pairs solving the same problem, so a bespoke implementation can be swapped for another field's standard, specialized solver. On a benchmark of 18 method families across 109 papers, the skeleton lifts cross-domain retrieval average precision over the abstract from 0.222 to 0.513, and the whole fingerprint reaches 0.557. Strikingly, four trained scientific embedders all fall below plain abstract+TF-IDF: they encode topical and citation similarity, the wrong signal for this task. The gain is the representation: the abstract-to-skeleton swap lifts every embedder, and the pipeline is one cached LLM call per paper plus a cheap embedder. An interventional re-skin / math-edit test shows the fingerprint tracks the computation, not the field. On a 501-paper wild corpus, known twins dominate the top of the ranking (23 of the top 30); with planted pairs excluded from the results, three blind LLM judges rate 3 of the top 5 and 8 of the top 30 pairs genuine import candidates, and 0 of 30 random ones. The human verification is the four executed imports: in one, an open standard solver reproduces a bespoke clinical dosing engine's output. We release the benchmark, the code, and the distillation prompt.

cs.DL↗