Thales's Prediction of a Solar Eclipse

Stephenson, F. R.; Fatoohi, Louay

doi:10.1177/002182869702800401

Cited by 13 publications

(2 citation statements)

References 4 publications

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“…Understanding nature has been a human endeavor since early existence. Indeed, the ancient Greek Thales of Miletus correctly predicted a solar eclipse occurring on May 28th, 585 BC, a date the great Isaac Asimov suggests to be the birth of science [32,21]. In this work, we focus on the discovery of dynamical systems with given states, where finitely many discrete measurements are used to approximately recover the unknown dynamical system -a data-driven discovery of dynamics [3,29,16].…”

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confidence: 99%

Discovery of Dynamics Using Linear Multistep Methods

Keller¹,

Du²

2019

Preprint

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Linear multistep methods (LMMs) are popular time discretization techniques for the numerical solution of differential equations. Traditionally they are applied to solve for the state given the dynamics (the forward problem), but here we consider their application for learning the dynamics given the state (the inverse problem). This repurposing of LMMs is largely motivated by growing interest in data-driven modeling of dynamics, but the behavior and analysis of LMMs for discovery turn out to be significantly different from the well-known, existing theory for the forward problem. Assuming the highly idealized setting of being given the exact state, we establish for the first time a rigorous framework based on refined notions of consistency and stability to yield convergence using LMMs for discovery. When applying these concepts to three popular M −step LMMs, the Adams-Bashforth, Adams-Moulton, and Backwards Differentiation Formula schemes, with M ∈ N, the new theory suggests that Adams-Bashforth for 1 ≤ M ≤ 6, Adams-Moulton for M = 0 and M = 1, and Backwards Differentiation Formula for all M are convergent, and, otherwise, the methods are not convergent in general. In addition, we provide numerical experiments to both motivate and substantiate our theoretical analysis.

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confidence: 99%

Discovery of Dynamics Using Linear Multistep Methods

Keller¹,

Du²

2019

Preprint

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“…The most famous battle in this regard is the one between the Lydians and the Medians, fought on 28 th May 585 BCE on the banks of the river Halys in central Turkey. The eclipse most likely a total was taken as an ill omen of the Sun and caused the warring armies to lay down the arms and negotiate an armistice (Stephenson and Fatoohi, 1997;Yazdi, 2008).…”

Section: Introductionmentioning

confidence: 99%

Historical Note: Reactions of Emperor Bahadur Shah Zafar and Laureate Mirza Ghalib to the Celestial Events during 1857-1858

Kapoor¹

2018

Indian Journal of History of Science

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The revolt against the British broke out at Meerut on 10 th May 1857 that soon turned into a Great Uprising and shook the foundations of the colonial power in India. A conjunction of Mars and Saturn took place in July 1857. A solar eclipse occurred on 18 th September 1857, two days before the capture of Delhi by the British. There followed a lunar eclipse, on 28 th February 1858. Then a comet brightened up in the evening skies only days before the British Crown was about to take India in its fold on 1 st November 1858. How Mughal Emperor Bahadur Shah Zafar (1775-1862), central to the upheaval, and the laureate Mirzā Ghālib (1797-1859), a remote observer, reacted in such a scenario is central to our theme. Z. afar was a superstitious man and had a spiritual incline. What is unique is that he had never mixed up the outcome of the war with the celestial events and left it to Almighty. That he was unaware of these events is difficult to believe. Ghālib was a skeptic and came to believe the celestial events as signals of divine wrath. In the process we discover an unexplored side of Mirzā Ghālib and his grasp of astronomy.

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