Blindspots of empiricism in the discovery of chaos theory

Brett Park

doi:10.1016/j.shpsa.2026.102133

Home/Archive/arXiv

arXiv · 2603.07684

Blindspots of empiricism in the discovery of chaos theory

Brett Park

View original source ↗Read source document ↗Export metadata ↓

Abstract

Chaos theory is a branch of classical physics, founded in the 1960s-70s, that studies systems whose solutions are sensitively dependent on their initial conditions. For many, it is surprising that chaos theory arrived so late. However, through the work of Henri Poincar\'e, we know that much of the math of chaos was understood by some 70 years prior. Furthermore, through the writings of Poincar\'e's colleagues -- Jacques Hadamard and Pierre Duhem -- we also see a detailed understanding of the chaos found in his work. They also have explicit reasons of why the math of chaos was to be ignored. It was a strict form of empiricism -- positivism -- causing them to label chaos as ``useless'' and ``meaningless'' mathematics because it was thought to be ungrounded in experience. In this paper, I describe how the empiricist tenets of positivism exiled chaos from physics following Poincar\'e.

Explore related subjects

physics.hist-ph nlin.CD

Keep this discovery

BibTeX RIS

Brett Park. 2026-03-08. Blindspots of empiricism in the discovery of chaos theory. https://doi.org/10.1016/j.shpsa.2026.102133

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

KEEP EXPLORING

Related papers

arXiv2026

Scientific Promise

Scientists constantly face decisions about what lines of research to pursue. This Element introduces the philosophical debate about scientific pursuitworthiness. It explains how it can be rational to pursue a theory even if the theory is less well supported than its rivals, and it discusses existing philosophical frameworks for guiding pursuit decisions. The Element also develops a new perspective. Existing accounts focus predominantly on theories, while experiments are largely neglected. This is an important shortcoming. Theoretical promise depends on experimental promise, and experimental promise raises questions of its own. Drawing on the epistemology of experimentation, the Element advances an account of experimental pursuitworthiness. It is argued that such pursuitworthiness depends on experimental virtues like a clear signal and simplicity of design. Moreover, the kinds of uncertainty that constrain the assessment of scientific pursuits are examined. Finally, the Element highlights open questions in the philosophy of scientific pursuitworthiness.

physics.hist-ph↗

arXiv2026

Is Black Hole Evaporation Prediction Friendly?

Manchak and Weatherall (2018) formulate the black hole information paradox as a failure of predictability in black hole evaporation spacetimes, diagnosed by non-global hyperbolicity. I offer a strategy for resolving this paradox. I argue that failures of predictability in black hole evaporation are not well diagnosed by non-global hyperbolicity. I then consider two weakenings of global hyperbolicity: prediction and retrodiction friendliness, the failure of which could ground a new paradox. However, deidealized black hole evaporation models can be prediction and retrodiction friendly. Therefore, the information paradox cannot be based upon failures of global hyperbolicity, nor either retrodiction or prediction unfriendliness.

physics.hist-ph↗

arXiv2026

The Crab Nebula progenitor: recovering the 1054 AD supernova event as galactic Gamma-ray burst

In 1054 AD a daytime star appeared in the constellation of Taurus, for three weeks, and it was reported in various sources from Europe to China/Japan: it was one of the few documented galactic supernovae of the last two millenia. This paradigm has been established about sixty years ago, as the comprehension of the physics of supernovae progressed with enough observational data. The Gamma-ray bursts were discovered in the same period, but only in the past few years have their observations become daily and their distances have been fully understood as cosmological. After the explosion, the exponential decay of the luminosity in gamma-rays and X-rays has been followed with telescopes onboard dedicated satellites. Also the exponential decay of the afterglow's optical and radio frequencies have been observed with the largest optical and radio telescopes. Within the binary-driven hypernova framework, successful in explaining all the observed phases of the Gamma-ray bursts, the universal exponential decay can be extended to 1000 years after the burst, to account for the present values of Gamma and X-rays as well as optical and radio frequencies of the Crab Nebula. Both the daytime visibility of the burst, and the simultaneous radiation plagues appeared in Constantinople and Cairo is a strong evidence of the presence of Gamma-rays in the lower atmosphere, coming from the same source originating the Crab nebula. The association to the daytime visibility of that star and the following plague meets exactly the etymology of the word dis-aster, bad star.

physics.hist-ph↗