arXiv subjects

Ari Belenkiy

Publications and source records attributed to Ari Belenkiy.

6 recordsLinked to original sources

arXiv2016

Groping Toward Linear Regression Analysis: Newton's Analysis of Hipparchus' Equinox Observations

In February 1700, Isaac Newton needed a precise tropical year to design a new universal calendar that would supersede the Gregorian one. However, 17th-Century astronomers were uncertain of the long-term variation in the inclination of the Earth's axis and were suspicious of Ptolemy's equinox observations. As a result, they produced a wide range of tropical years. Facing this problem, Newton attempted to compute the length of the year on his own, using the ancient equinox observations reported by a famous Greek astronomer Hipparchus of Rhodes, ten in number. Though Newton had a very thin sample of data, he obtained a tropical year only a few seconds longer than the correct length. The reason lies in Newton's application of a technique similar to modern regression analysis. Newton wrote down the first of the two so-called 'normal equations' known from the ordinary least-squares (OLS) method. In that procedure, Newton seems to have been the first to employ the mean (average) value of the data set, while the other leading astronomers of the era (Tycho Brahe, Galileo, and Kepler) used the median. Fifty years after Newton, in 1750, Newton's method was rediscovered and enhanced by Tobias Mayer. Remarkably, the same regression method served with distinction in the late 1920s when the founding fathers of modern cosmology, Georges Lemaitre (1927), Edwin Hubble (1929), and Willem de Sitter (1930), employed it to derive the Hubble constant.

physics.hist-ph↗

arXiv2014

Discovery of Hubble's Law: an Example of Type III Error

Recently much attention has been paid to the discovery of Hubble's law: the linear relation between the rate of recession of the distant galaxies and distance to them. Though we now mention several names associated with this law instead of one, the motivation of each remains somewhat obscure. As it is turns out, two major contributors arrived at their discoveries from erroneous reasoning, thus making a case for a Type III error. It appears that G. Lemaitre (1927) theoretically derived Hubble's Law due to his choice of the wrong scenario of the Universe's evolution. E. Hubble (1929) tested the linearity law not based on Lemaitre's non-static model, but rather a cumbersome extension of de Sitter's static theory proposed by H. Weyl (1923) and L. Silberstein (1924).

physics.hist-ph↗

arXiv2013

"The Waters I am Entering No One yet Has Crossed": Alexander Friedman and the Origins of Modern Cosmology

Ninety years ago, in 1922, Alexander Friedman (1888-1925) demonstrated for the first time that the General Relativity equations admit non-static solutions and thus the Universe may expand, contract, collapse, and even be born. The fundamental equations he derived still provide the basis for the current cosmological theories of the Big Bang and the Accelerating Universe. Later, in 1924, he was the first to realize that General Relativity allows the Universe to be infinite. Friedman's ideas initially met strong resistance from Einstein, yet from 1931 he became their staunchest supporter. This essay connects Friedman's cosmological ideas with the 1998-2004 results of the astronomical observations that led to the 2011 Nobel Prize in Physics. It also describes Friedman's little known topological ideas of how to check General Relativity in practice and compares his contributions to those of Georges Lemaitre. Recently discovered corpus of Friedman's writings in the Ehrenfest Archives at Leiden University sheds some new light on the circumstances surrounding his 1922 work and his relations with Paul Ehrenfest.

physics.hist-ph↗

arXiv2008

Stirring Astronomy into Theology: Sir Isaac Newton on the Date of the Passion of Christ

It is known that Sir Isaac Newton suggested a date for the Passion of Christ in the posthumously published "Observations upon the Prophecies of Daniel and the Apocalypse of St. John" (1733). What was not known is that the first attempts to find that date were made during the early period of his life. The Jewish National and University Library in Jerusalem contains two undated drafts in Latin under the same title, "Rules for the Determination of Easter", grouped as Yahuda MS 24E. The earlier draft contains multiple references to the virtually forgotten "De Annis Christi" (1649), written by Villum Lange, the 17th century Danish astronomer and theologian, who might have been Newton's first mentor on the Jewish calendar tradition. The second draft shows not only Newton's close acquaintance with Maimonides' theory of first lunar visibility, but also his attempt to simplify the latter's criteria by introducing different, more practical parameters. These "astronomical exercises", announced in a 1673 book, were likely intended to appear as an appendix to Nicholas Mercator's 1676 book. Both of Yahuda 24E's drafts contain an astronomical table with the solar and lunar positions for years 30-37, which Newton used to decide on the year and date of the Passion. The astronomical data comes from either 1651 "Harmonicon Coeleste" or 1669 "Astronomia Britannica" by Vincent Wing, a semi-forgotten astronomer of the seventeenth century. This makes Yahuda 24E one of the earliest of Newton's drafts, likely written in 1669-73 and certainly not later than 1683/4. A comparison of the two drafts of Yahuda 24E shows that in the later one, Newton changed his allegiance from St. John's chronology of the Passion to that shown in the synoptic gospels.

physics.hist-ph↗

arXiv2006

The Geometry of Stochastic Reduction of an Entangled System

We show that the method of stochastic reduction of linear superpositions can be applied to the process of disentanglement for the spin-0 state of two spin-1/2 particles. We describe the geometry of this process in the framework of the complex projective space

quant-ph↗

arXiv2001

Inner Market as a "Black Box"

Each market has its singular characteristic. Its inner structure is directly responsible for the observed distributions of returns though this fact is widely overlooked. Big orders lead to doubling the tails. The behavior of a market maker with many or few ``friends'' who can reliably loan money or stock to him is quite different from the one without. After representing the inner market ``case'' we suggest how to analyze its structure.

cond-mat.dis-nn↗