Some notes about the possibility of a mathematical theory of History

I will present some general remarks and some personal opinions and findings (with a constant concern for accuracy and objectivity) about the attempts at mathematizing History , historical events , processes and phenomena.

My many readings (see my various book pages and the books I have read) and my analysis of History made me realize that important historical events and phenomena are (highly) periodic , and that exact correspondences (or similarities or “homologies” , one of these terms could be chosen, used  and defined) can be found between historical events separated by definite periods of time .

The history of humanity can be considered as the result of the interactions between the lives and actions of human beings  moving and acting in time. All humans have a role to play in the unfolding of historical events , but great men (and women) and great thinkers/scientists/reformers constitute the main group of humans who change and drive historical phenomena and happenings across cultures , nations and empires.

Evolution and progress take place in human history , such as technological/scientific progress, the increase in the global human population over millennia and the increase in the surface of political entities, from city-states to nation-states and to bigger entities , etc, but there are also general principles and definite periodicities and regularities in world history. Among these regularities are the stages or phases of gradual growth and decline through which most great powers and empires pass as they rise/fall and go up and down in time. Certain essential periodicities or cycles in history are accompanied by a change or transmutation in values (“moral” , behavioral , sexual, etc).
Relevant concepts can be defined such as the notion of bi-millenary (exact) correspondence and of bi-millenary periodical return of historical events. I will explain and clarify these concepts more when I have time in future writings.

Some philosophical and religious theories talk about eternal return/recurrence and cyclical time (the notion of eternal return constantly permeates the philosophy of Nietzsche), but these notions are not defined in a precise or scientific way.

I think that Mathematics and the scientific method , i.e observing phenomena and collecting data, creating hypotheses with the adequate mathematical model, experimental/empirical verification of these hypotheses and building  coherent theories, can be used in and applied to human history, provided that this is done in the proper and correct way. Historical chronology plays an important role, and the chronology of events before the Common or Christian era ought to be revised and corrected.

Another prerequisite for the impartial and objective study of history is to abandon preconceived ideas and to have a global perspective of human history , avoiding euro-centrism , afro-centrism and all kinds of ethnocentrisms , and avoiding to get stuck in certain habits such as classifying people and cultures into Western and non-Western. One should take into account the fact that geopolitical groupings and alliances change with the passing of time , centuries and decades.

A new discipline called Cliodynamics was created in the last decade . It is an area of research using mathematical , quantitative approaches and modelings to explain historical processes and societies. The practitioners of this discipline have made some interesting observations about historical events and have tried to formulate mathematically backed theories to interpret historical facts , however I think they have not found or discovered the right , convenient , correct and/or precise way to mathematize History and historical phenomena .

If the right mathematical theory of human history can be elaborated, using the scientific method and testing hypotheses in history could be equivalent to and lead to the (precise) prediction of important events taking place in the future of humankind.

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Books about physics, astrophysics and astronomy regarded as important classics

This post is mostly inspired (with some additions and modifications) from and answer I wrote at quora.com .

I will try to give a list of famous , influential books or classic books having a significant historical importance in the fields of physics , astrophysics and astronomy . It’s a somewhat extensive list but it’s not exhaustive.

Starting with Antiquity :

Then advancing to more recent times:

Al Sufi stars

Copernicus book

Below is a page from the Astronomia Nova (in 1609) showing the three models of planetary motion known in the seventeenth century (free image from Wikipedia) :

Astronomia Nova

Newton's Principia

Hydrodynamica

Carnot reflexions

  • Recherches sur la théorie des quanta (Researches on the quantum theory) , and The Current Interpretation of Wave Mechanics: A Critical Study , by Louis de Broglie .
  • Collected papers , The interpretation of Quantum Mechanics , and Statistical Thermodynamics , by Erwin Schrödinger .
  • The Physical Principles of the Quantum Theory , by Werner Heisenberg .
  • Books and papers by Paul Dirac , such as The Principles of Quantum Mechanics and Lectures on Quantum Field Theory .
  • Space, Time and Gravitation: An Outline of the General Relativity TheoryThe Internal Constitution of Stars , and The Nature of the Physical World , by Arthur Eddington .
  • Problems of Cosmology and Stellar Dynamics , An Introduction to the Kinetic Theory of Gases , and  The Growth of Physical Science , by James Hopwood Jeans .
  • The Theory of Sound , by John William Strutt, 3rd Baron Rayleigh .
  • Problems of Atomic Dynamics , Atomic Physics , Principles of Optics , Experiment and Theory in Physics , and A General Kinetic Theory of Liquids , by Max Born .
  • Books and papers by David Bohm , such as Quantum Theory , Causality and Chance in Modern Physics , The Undivided Universe.

Some more recent well known , insightful and/or widely used books would include :

  • The Large Scale Structure of Space-Time , by Stephen Hawking and George F. R. Ellis .
  • Speakable and Unspeakable in Quantum Mechanics , by John Stewart Bell .
  • Classical-Mechanics , by Herbert Goldstein .
  • Classical Electrodynamics , by J.D. Jackson .
  • Galactic Dynamics , by Binney and Tremaine .
  • The Quantum Theory of Motion: an account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics , by Peter Holland .
  • Photons and Atoms: Introduction to Quantum Electrodynamics , by Claude Cohen-Tannoudji , Gilbert Grynberg and Jacques Dupont-Roc .
  • Introduction to Elementary Particles , by D.J. Griffiths .
  • Condensed Matter Field Theory , by Alexander Altland .
  • The Standard Model and Beyond , by Paul Langacker .
  • The Road to Reality , by Roger Penrose .
  • Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law , by Peter Woit .
  • The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next , by Lee smolin .
  • Farewell to Reality: How Modern Physics Has Betrayed the Search for Scientific Truth , by Jim Baggott .

Additional relevant links :

https://en.wikipedia.org/wiki/Hi…

https://en.wikipedia.org/wiki/Hi…

Astronomy in the medieval Islamic world

Indian astronomy

Chinese astronomy

Books about mathematics regarded as noteworthy classics

This post is taken (with some modifications from an answer I gave at quora.com  .

Classic books or classics may refer to great and historically important books , or to books widely popular , read and used ,or both . I will try to mention both types of books.
I will cite first a number of books which I think are of primary importance in the history of mathematics , and therefore are generally regarded as classics . This is not a exhaustive list .
Let’s start with some books from Antiquity :
Moving a few centuries later to modern times :
Some recent modern and well known math books that may be regarded as classics :
See also the following links :

The Lagrangian of the Standard Model of particle physics

I will present some notes and explanations related to the Standard Model of particle physics and its Lagrangian . The text in this post is inspired from two answers I gave at quora.com .

The Standard model and its Lagrangian form a vast topic . I will attempt to give relevant and accurate information about it.

The story of the Standard Model started in the 1960s with the elaboration of the theory of quarks and leptons  , and continued for about five decades until the discovery of the Higgs boson in 2012.
For a timeline of the history of the Standard Model see the Modern Particle Theory timeline .
The formulation of the Lagrangian of the Standard Model with its different terms and parts mirrored the theoretical and experimental advances associated with particle physics and with the Standard Model.

The Lagrangian function or Lagrangian formalism is an important tool used to depict many physical systems and used in Quantum Field Theory . It has the action principle at its basis .

In simple cases the Lagrangian essentially expresses the difference between the kinetic energy and the potential energy of a system .

The Standard Model of particle physics describes and explains the interactions between the essential components and the fundamental particles of matter , under the effect of the four fundamental forces: the electromagnetic force , the gravitational force , the strong nuclear force , and the weak (nuclear) force.
However , the Standard model is mainly a theory about three fundamental interactions , it does not fully include or explain gravitation .
The Standard model (or SM) is  a gauge theory representing fundamental interactions as changes in a Lagrangian function of quantum fields.  It depicts spinless , spin-(1/2) and spin-1 fields interacting with one another in a way governed by the Lagrangian which is unchanged by Lorentz transformations.

The Lagrangian density or simply Lagrangian of the Standard Model contains kinetic terms , coupling and interaction terms (electroweak and quantum chromodynamics sectors) related to the gauge symmetries of the force carriers (i.e. of the elementary and fundamental particles which carry the four fundamental interactions) , mass terms , and the Higgs mechanism term .

Explicitly , the parts forming the entire Lagrangian generally consist of :
Free fields : massive vector bosons , photons , and leptons.
Fermion fields describing matter.
The Lepton-boson interaction.
Third-order and fourth order interactions of vector bosons.
The Higgs section.

Leptons are the elementary particles not taking part in strong interactions.
All leptons are fermions. They include the electron , muon , and tauon , and the electron neutrino , muon neutrino , and tauon neutrino.
All leptons are color singlets , and all quarks are color triplets.

In the Standard model , the Higgs mechanism provides an explanation for the generation of the masses of the gauge bosons via electroweak symmetry breaking.

Different reference works , books , e-books or textbooks use different or slightly different notations and symbols to describe or designate the entities and terms within the Lagrangian of the SM .

Below is a detailed image of the Lagrangian of the Standard Model  (Source: http://einstein-schrodinger.com/Standard_Model.pdf ).
However I have rearranged it and modified it with the help of Photoshop to make it look more presentable and more readable.

lagrangian of the standard model

The Lagrangian function in the Standard Model , as in other gauge theories , is a function of the field variables and of their derivatives.

G_ {\mu \nu} is the gauge field strength of the strong SU(3) gauge field.
Gluons are the eight spin-one particles associated with SU(3).
A particle which couples to the gluons and transforms under SU(3) is called ‘colored’ or ‘carrying color’.
Gluons and quarks are confined in hadrons.

W_ {\mu \nu} is the gauge field strength of the weak isospin SU(2) gauge field .

The field strength tensor W_ {\mu \nu} is given by :

field strength tensor

where g_2 is the electroweak coupling constant , a dimensionless parameter.

The charged W^+ and W^- bosons and the neutral Z boson represent the quanta of the weak interaction fields between fermions , they were discovered in 1983 .

B_ {\mu \nu} is the gauge field strength of the weak hypercharge U(1) gauge field.
The field strength tensor B_ {\mu \nu}  is given by :

B_ {\mu \nu} = \frac {\partial B_ {\nu}} {\partial\mu} - \frac {\partial B_ {\mu}} {\partial\nu}

In the Standard model , electrons and the other fermions are depicted by spinor fields .
The group U(1) is the set of one-dimensional unitary complex matrices .
U(1) represents the symmetry of a circle unchanged by rotations in a plane.

SU(2) is called ‘the special unitary group of rank two’. It is a non commutative group related to SO(3) , the sphere symmetry in 3 dimensions.
SU(2) is the set of two-dimensional complex unitary matrices with unit determinant.

SU(3) , the special unitary group of rank three , is used in quantum chromodynamics (QCD) .
SU(3) is the set of three-dimensional complex unitary matrices with determinant equal to 1 .
The natural representation of SU(3) is that of 3×3 matrices acting on complex 3D vectors.
The generators of the group SU(3) are eight 3×3 , linearly independent , Hermitian , traceless matrices called the Gell-Mann matrices . These generators can be created from Pauli spin matrices (which are used with the group SU(2) ) .

The SM Lagrangian displays invariance under SU(3) gauge transformations for strong interactions , and under SU(2)xU(1) gauge transformations for electroweak interactions.

The electromagnetic group is not directly the U(1) weak hypercharge group component of the standard model gauge group. The electric charge is not one of the basic charges carried by particles under the unitary product group SU(3)xSU(2)xU(1) , it is a derived quantity.

All the masses vanish in the absence of the Lagrangian term related to the Higgs , due to the invariance of SU(3)xSU(2)xU(1) .

In some texts the gauged symmetry group of the SM is written with subscripts such as:
\text {SU} _c (3)\times\text {SU} _L (2)\times U_Y (1)
In the notation above , the subscript ‘c’ denotes color.
The subscript ‘L’ denotes left-handed fermions.
The subscript ‘Y ‘  distinguishes the group related to the quantum number  of weak hypercharge , expressed by the letter Y , from the group associated with ordinary electric charge, expressed by Q .
U_ {\text {em}} (1) denotes the electromagnetic group.

The Higgs field in the Standard model is a complex scalar doublet. It is generally represented by :

 Higgs field doublet

In the image of the SM Lagrangian above , the Higgs field has the form

Higgs field form

The field h(x) is real .

In the SM Lagrangian image above , \phi _ 0  is equal to v .

As an additional note , the  equation of the Lagrangian  is usually made of a definite number of terms and Lagrangians.
In order to make such an equation look less like a big behemoth and make it more compact ,  it would be simpler to view it or write it first as the sum of Lagrangians :

\mathcal{L}=\mathcal{L}_1+\mathcal{L}_2+\text{...}+\mathcal{L}_n

 or equivalently :

\mathcal {L} = \sum _ {i = 1}^n\mathcal {L} _i

Then each Lagrangian in the equation could be expanded and explained.

Some helpful resources about the Standard Model and its Lagrangian :
Standard Model

The Standard Model of Particle Physics

Standard Model (mathematical formulation)

http://arxiv.org/pdf/hep-ph/0304186v1.pdf

Gauge Theory of Weak Interactions: Walter Greiner, Berndt Müller: 9783540878421: Amazon.com: Books

The Structure and Interpretation of the Standard Model, Volume 2 (Philosophy and Foundations of Physics): Gordon McCabe: 9780444531124: Amazon.com: Books

The Standard Model: A Primer: Cliff Burgess, Guy Moore: 9781107404267: Amazon.com: Books

An Introduction to the Standard Model of Particle Physics: W. N. Cottingham, D. A. Greenwood: 9780521852494: Amazon.com: Books

The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics: Robert Oerter: 9780452287860: Amazon.com: Books

Here is also a link to one of the  important papers in the history of the Standard Model written in 1967 by Weinberg and entitled ‘A Model of Leptons’ :
http://physics.princeton.edu/~mcdonald/examples/EP/weinberg_prl_19_1264_67.pdf

About Zeus , Prometheus , and the punishment of the latter- Part Two

I will continue my analysis, ideas and comments concerning the punishment of Prometheus, how it was viewed by various writers and thinkers, and what likely happened between Prometheus and Zeus.

A painting of Titian in 1548-1549 ( see the image below), representing the giant Tityus being punished in a way similar to that by which Prometheus was punished, was mistakenly thought to represent Prometheus  for decades and even centuries, and was an inspiration for later painters who represented Prometheus (based on the erroneous identification of Titian’s painting). Tityus was punished for having violated or having tried to violate Leto/Latona, the mother of Apollo and Artemis/Diana.

Tityus-by-Titian

The Punishment of Tityus , by Titian

The painter José de Ribera  also made a painting of the punishment of Tityus in 1632. 

Perhaps if the details of the story and the accurate sequence of events which led to the theft of fire by Prometheus were known ( see my previous post about the same topic), they would show and prove that Prometheus did not help or benefit anyone by his theft. The actions of Prometheus were caused by envy, jealousy, greed and treachery, he misused the thing he had stolen, played with it carelessly or ignorantly with no beneficial or creative results, and consequently he deserved to be chastised just as Tityus and other characters such as Tantalus deserved to be punished for their actions .

The view that Prometheus was a good benefactor and an important figure started at the end of the eighteenth century and the beginning of the nineteenth, when a number of known writers, poets and thinkers more of less promoted this trend, which was partly based on the misinterpretation of the play Prometheus Bound (presumably) by Aeschylus. I’ll take a look at some of these views and comment on them.

In his youth , Johann Wolfgang von Goethe wrote a poem about Prometheus. In Goethe’s poem, Prometheus mentions his childhood and the disappointment of the prayers he addressed to the gods. From the poem it looks as if Prometheus had a deep feeling which led him to free himself from the gods.
This statement bears an amount of anachronism and contradiction with the mythological story of the gods: when Prometheus was a child , the future gods were still overpowered and ‘swallowed’ by their father (the Titan Cronus), then when Zeus grew up he stood up to his father and freed his siblings. As a child and as a man too, Prometheus followed the older established order of the Titans and must have followed any form of older religion or mentality or way or thinking related to the Titans. According to the mythological stories he was of the same generation as Zeus and the Olympians gods but he stayed with the old order of the Titans. It was Zeus/Jupiter who created a newer order , gave his brothers and sisters their positions according to their powers and abilities, and brought stability to the world. Prometheus didn’t accept this new order which was based on new ideas related to justice and pragmatism. If Prometheus was praying to anyone, then it is more reasonable to suppose that he prayed to whatever deities the Titans prayed to, and he disliked Zeus and his family and offspring for leaving the old ways of praying and thinking of the Titans and for innovating and creating new ways.
With time Goethe  abandoned to a certain extent his interest for or liking of Prometheus. As he grew old, Goethe was compared by several writers to an Olympian god and to Zeus himself.
For example , Frederick Engels wrote in Feuerbach: The roots of the socialist philosophy :
“Goethe and Hegel, each of them was an Olympian Zeus in his own sphere, but they were neither of them quite free from German philistinism.”
And the German romantic writer Jean Paul (1763-1825) described Goethe as “the Olympian who rules the world from his throne” .

In the nineteenth century C.E., a number of writers and philosophers made unfounded allegations and extrapolations and began a certain trend which pictured Prometheus as a figure of free thought and anti-religion and a hater of all the gods. The fact is Prometheus himself was called a god and a Titan god .

When in some of his first writings Karl Marx tried to make of Prometheus a champion of anti-religion and a martyr of philosophy, portraying him as a freethinker who despised all gods, many critical remarks are in order : Marx read the play by Aeschylus and understood it literally, not taking into account that Aeschylus used a good amount of irony and intended to show Prometheus as delusional and arrogant. Marx also didn’t consider the fact that Prometheus was a Titan attached to an old form of ‘nobility’ , an old way of thinking and old traditions. When Prometheus said he hated all the gods , it’s reasonable to think that he meant by gods the people related to Zeus who were called (Olympian) gods and who represented a new order and a new way of thinking. He hated the Olympian gods, but he surely didn’t hate the Titan gods. In fact Prometheus was attached to these older Titan gods who stretched and ‘over-reached’ themselves more than they could and were limited in their sphere of action and were defeated, and he followed whatever old form of religion or belief which was accepted by the Titans. So the conclusions made by Marx about Prometheus’s freethinking and ‘atheism’ are extrapolated and unproven conjectures which seem to project the wishful ideals of Marx onto Prometheus.

Nietzsche tried for a while to interpret the story of Prometheus as involving someone who stood against divine power (i.e Zeus), someone who opposed the morality related to Christianity and Judaism, which was based on sin, and who showed that even sacrilege and theft can be dignified. Again I think this is wishful thinking by Nietzsche and an attempt to project on Prometheus his own aspirations , ideas and opinions. Prometheus disappeared from Nietzsche’s work together with the appearance of the philosopher’s new central character : the Übermensch.

I think the writer who went the furthest in his glorification of Prometheus was Percy Bysshe Shelley , who wrote the drama Prometheus Unbound and published it in 1820 .

The author of The Necessity of Atheism chose the wrong person to elevate to the post of hero or champion. Shelley ought to have taken into account the very plausible fact that Prometheus was most likely an intellectual mediocrity and someone who was attached to old traditions, old mentalities and probably an old form of religion related to the group of people he belonged too, the ones who were subsequently called Titans, who outreached themselves, were limited in their thinking and their actions, and who consequently lost their dominion and power and were defeated by Zeus and his siblings. Prometheus had nothing to do with freethinking , advanced thinking or technological innovation. He was no better than his fellow Titans (who were punished) other than by the fact that he tried to use guile and trickery, but he didn’t succeed at what he did. He did not benefit others by his act of theft, was outsmarted by Zeus and got what he deserved.

The poet or writer has the responsibility to tell the truth and give a fair and reliable account of past events, even if he does that in a literary, stylish or figurative way.
While calling Zeus/Jupiter “The Oppressor of Mankind” in his play, Percy Bysshe Shelley must have known that Zeus was called “The Lord of Justice”, “The patron of hospitality and guests” , “The keeper of oaths” , “Soter ,(Savior)”, “Jupiter Optimus Maximus Invictus” ( by the Romans), along with too many other epithets and names.
Shelley wrote a Hymn of Apollo. He praised the son but disliked the father, although Apollo’s father was known to be the ruler, the greatest and the most important of the Olympian gods . Perhaps some inconsistency is to be noticed here.
Moreover, according to Apollo’s mythology, after he was born he was known to have said : “May the lyre and the bow be dear to me forever , and I will prophesy to mortals the unerring will of Zeus”.
Shelley took a story told in ancient myths, poems, narratives and religions, a story which had plausibly true historical events as its basis, and he twisted that story and made the one who was known to have never been defeated or dethroned (i.e. Zeus/Jupiter , Optimus Maximus ,Victor, Invictus , Stator , as he was called by the Romans ) end up being vanquished. He also made the envious mediocrity who was defeated and justly punished look like the victor in events and conditions which never took place. He tried to represent Prometheus as some sort of dissenting intellectual or innovator who requested reforms, while the one who brought real reforms, changes and new ideas and equitable rules was Zeus/Jupiter, whereas Prometheus was a jealous, unexceptional individual following the older, established ways and traditional ideas of the Titans.
By misinterpreting the Prometheus Bound tragedy and by writing Prometheus Unbound, Shelley has likely done more harm than good, in the sense that he has recklessly distorted ancient known stories and events and he has acted irresponsibly, without caring about the veracity or the consequences of his writings.

As an additional note , according to Wikipedia  , “Paul Johnson, in his book Intellectuals , describes Shelley in a chapter titled “Shelley or the Heartlessness of Ideas “. In the book Johnson describes Shelley as an amoral person, who by borrowing money which he did not intend to return, and by seducing young innocent women who fell for him, destroyed the lives of everybody with whom he had interacted, including his own.”
This is to be contrasted with the mythological tales and stories about Zeus/Jupiter, the lord of justice who gave each his due, who ‘easily humbles the proud and raises the obscure, and easily straightens the crooked and blasts the proud’ (from Hesiod’s Works and Days).
Zeus had numerous relationships with many women, but he was known for taking care of and protecting the women who birthed his children, and his offspring , from Hercules to Apollo and Perseus and others, were regarded as heroes, gods, demi-gods and founders of dynasties who were helpful and beneficial to mortals and humans. Although he sometimes had disputes with his wife Hera, Zeus knew she was his wife, the principal and most important woman for him, and he always treated her accordingly , and always managed to get along and reconcile with her.

To be complete one should  also consider the point of view of Euhemerism , and it’s a relevant and important one .
Euhemerism essentially states that gods were great men who were deified after their death, and seeks the source of mythology in history .
According the this view, Prometheus would appear as a man with little preparation or with limited, misused potentiality for greatness or creativity, who lived alongside a really great man who was later called Zeus or Jupiter ( he was known by other names in other places and religions too), and who by jealousy, hubris, conceit, attachment to an old established order and old ways of thinking, and by misguided actions, betrayed and tried to trick and hurt the very great man who was his contemporary. Prometheus possibly helped Zeus or worked under his supervision for a short period of time, then he stole from him by jealousy and greed and was deservedly punished for it.
As a very great man of the past, Zeus/Jupiter must have had the most advanced way of thinking, the most advanced teachings and the most advanced knowledge and ‘theories’ in the world he lived in.
I also think Zeus/Jupiter was the same person as one of the first important biblical patriarchs mentioned in the Old Testament, but his story was somewhat modified. Perhaps I will expand and develop this idea in the future.

Sometimes a man attached to a religion or a set of rules and moral prescriptions comparable or even similar to those recommended by Christianity, and having limited abilities and living in the presence of a real great man and innovator, may by jealousy, greed, arrogance and conceit, break the rules he is supposed to be attached to, and steal from the great man he is jealous of, trying foolishly to show he is strong and brave, keeping the thing he stole to himself or in his abode, failing to do anything creative or useful with it, thus somewhat contradicting himself and proving to be worthy of being punished.
If Prometheus ought to be made the symbol of anything, then he ought to be considered as the symbol of mediocrity, envy, jealousy, greed, trickery, cheating, antis-science, anti-innovation and attachment to old traditional established ideas and to old ways of thinking and acting.

For about two centuries a number of writers have inflated the story of Prometheus and taken it in different directions. Consequently it can be said that they have been responsible of imagining, following and honoring a false idol, since they made him a symbol of things he had nothing to do with.
At times these were different and opposite ‘things’, such as being a symbol of irreligion and free thought, and being a symbol of religion more or less comparable to the founder of Christianity.

Perhaps these writers and thinkers should have taken the following guideline or principle into account:

When you don’t know the details of a (very ancient) story, or the sequence of events which caused something to take place, you should not jump into conclusions and produce speculative conjectures, project your own ideals or preconceptions on somebody, and/or make of somebody the symbol of things or qualities he has nothing to do with, especially when these conclusions and conjectures are based on uncertain and doubtful facts of the past, and when there are other facts or evidence providing more plausible and reasonable interpretations of the story or events in question.

As a consequence of all the arguments given above and in Part One of this topic, I think it is inappropriate and simply wrong to use the name of Prometheus for a series of books related to free thought and advanced cultural or philosophical subjects, because someone like Prometheus has simply nothing to do with these subjects. In fact I think it is someone with the intellect and the abilities of Zeus who would be more interested in and inclined towards reading books about advanced science, philosophy, and similar subjects .

The books and reference works I cited in my previous post about this topic are also relevant here.

I will add one more related reference work here:

The Justice of Zeus , by Hugh Lloyd-Jones .

This topic is likely to be continued in a third post.

The equations of electrodynamics , tensors , and gravitation-Second Part

I’ll start this continuation of the topic of a previous post by  an exposition and explanation of the concept of tensors in relativity physics  given by Albert Einstein , from his 1916 paper The Foundation of the General Theory of Relativity :

” The laws of physics must be of  such a nature  that  they apply  to systems of reference in any kind of motion.

The general laws of nature are to be expressed by equations which hold good  for all systems of coordinates, that is, are co-variant  with respect to any substitutions whatever (generally covariant).

Let certain things (” tensors “)  be defined with respect to any  system of  coordinates  by  a  number of functions of  the  coordinates , called  the  ” components ”  of the  tensor. There  are  then   certain  rules  by  which   these components can  be calculated   for  a new system of  coordinates , if they are known  for the original  system  of coordinates, and if  the  transformation  connecting  the two systems is known. The things  hereafter  called    tensors are further characterized by the fact  that the equations of transformation for their  components are linear  and  homogeneous.  Accordingly,  all  the components in  the  new system  vanish,  if  they all  vanish in the  original system. If,  therefore, a law  of nature is expressed  by equating all the components of a tensor to zero, it  is  generally covariant. By  examining the  laws of  the formation of  tensors, we acquire  the  means  of  formulating generally covariant laws. “

Source : The Principle of Relativity (Dover Books on Physics)
Einstein’s paper can also be found here:

The Foundation of the Generalised Theory of Relativity

I will deal in this post with the derivation of the Einstein field equations of General Relativity and with the related equations of motion.

As in the previous post , I will not show all the long and detailed calculations but I will give an overview of the equations , calculations and derivations .

We start with the derivation of the field equations free from the sources generating the field.The equations are deduced from the principle of least action.

A small remark : in the equations below , the symbol g written in two ways is the same letter in two different fonts , it represents either the metric tensor (with subscript or superscript) or the determinant of its matrix representation.

The action of the gravitational field is given by:

action gravitation

where χ is the gravitational constant appearing in Einstein’s field equations.
Ω is the product of the differentials of the coordinates.
In four-dimensional space we have :

d \Omega =\text{dx}^0 \text{dx}^1 \text{dx}^2 \text{dx}^3 

In the action integral above , The scalar curvature (or the Ricci scalar) R is related to the Ricci tensor by the equation R = gij Rij  .
And the Ricci tensor is related to the Riemann curvature tensor by the equation:

Ricci tensor

Hence we have:

gravitation action integral

The variation of the action yields:

variation of action

After calculation the first integral in the variation of the action above gives:

first integral in action

The third integral in the variation of the action is equal to zero:

third integral in action

And the variation of the action can be written as:

em-grav-001d

The variations δgij are arbitrary and the Einstein field equations independent of the sources generating the field
(  Rij – (1/2)gij R = 0 ) can be deduced from the integral above.

The action for matter and the electromagnetic field is given by:

action for matter

This action and its variation involve the Lagrangian density:

action variation

After integrating and calculating we get:

action calculation

Defining the energy momentum tensor (or stress–energy–momentum tensor ) by the relation:

energy momentum tensor

We get for the variation of the action:

action with stress energy tensot

The preceding results lead to the condition δ(Sg+Sme)=0 being written as:

action variation result

The equality above must remain valid for arbitrary variations of δgij  ,and we deduce :

field equations

which are the Einstein field equations of General Relativity.

The contravariant form of the energy-momentum tensor is given by the transformation :

contravariant energy momentum tensor

Below is a schematic description of the contravariant components of the energy-momentum tensor (image from Wikipedia) :

components of contravariant tensor

Note that of we take the more general form of the action :

action with cosmological constant

The field equations for the most general case would become:

field equations with cosmological constant

where λ is the cosmological constant .

The Einstein field equations are in agreement with the conservation of the energy-momentum tensor , which means its divergence is null:

null divergence

The energy-momentum tensor (mixed tensor) can be written as the sum of two terms:

The first one is of electromagnetic origin:

electromagnetic mixed tensor

The second one involves the presence of matter:

mixed tensor matter

The condition of null divergence can be written as:

null divergence two terms

After some calculations we get for the first term :

first term of divergence

And for the second term in the null divergence equation:

second term null divergence

By using the last two equations above , equation (1) can be written as:

em-grav-12

which is the equation of motion of a continuous distribution of charge inside a gravitational field and an electromagnetic field.

The references and sources in my Science books page and the problem solvers page can be viewed for books which I have read , worked out or consulted and which are related to the topics in this post.
I found the book by Jean-Claude Boudenot ( Electromagnetisme et gravitation relativistes ) helpful while I was studying these topics in the past.

About Zeus , Prometheus , and the punishment of the latter- Part One

At the beginning of this post I want to remark that Zeus (as well as  characters related to him) is the  name given by the ancient Greeks to ‘someone’ or to a deity who was followed or worshiped in many places  in the ancient World and around the Mediterranean region by different names . Zeus was called Jupiter by the Romans, Amon-Ra by the Egyptians , etc , and Greek mythology and religion had their origins in or were influenced by  other places or cultures : West Asia, the so-called Indo-Europeans , and most notably the Mediterranean and the Near East .
But I will generally use the Greek names since nowadays  they are the most widely known .

The story of Prometheus and the narration of his punishment  have been told and retold in different ways throughout the centuries. From Antiquity to the present , poets , writers, philosophers and various thinkers on the whole made contradictory assumptions, conjectures , explanations , extrapolations , comparisons  and conclusions related to the story of Prometheus. But if one looks closer and in depth at how the story has been told , one can find patterns or variations specific to certain periods in the telling of the story across different centuries.

The punishment inflicted by Zeus has been called by some modern authors ‘problematic’. But it would be less problematic if the facts about what happened and if the details of the story were known better. One of the difficulties is that the details of this story became unclear and imprecise with the passing of time , especially after the beginning of the Christian era.

Prometheus and Hercules

I have read extensively about this topic , and I will try to show by using reasonable and plausible arguments based on my readings of those who wrote about this subject that the reasons for and the cause of the chastening of Prometheus  have been misunderstood and misinterpreted , and his importance has been inflated and overestimated , mainly during the last two centuries .

The poet Hesiod (who lived around 750 BCE ) mentioned Prometheus in his Theogony and in The Works and Days
In the Theogony , Hesiod shows Prometheus as a lowly challenger of the omnipotence of Zeus and as a trickster.
In the Works and Days , Prometheus appears as the source of man’s misery. He is punished for using trickery , for stealing and breaking the law , and he is the one to blame for mankind’s fall.

It is to be noted that if the story of Prometheus has had a real earlier historical origin at its basis , then the oldest sources related to this story are usually the closest  to the actual events that took place ,  and they show what happened in a more accurate way compared to later narratives. Therefore the story as it is told by Hesiod largely presented Prometheus in his true colors more than other more recent accounts that came up later on.

There are other clues that shed light on the way Prometheus was viewed in Antiquity.
When people in Antiquity deified someone and built temples for him (or her , but here we’ll suppose it’s a man we’re talking about) , it was their way of showing and recognizing that the one they deified had done great , outstanding and important things and had a significant historical greatness and importance.
Ancient writers , such as Lucian in the second century CE , stated the fact that for centuries before and during the start of the the Christian era ( a period of probably more than two millennia) there was no temple of Prometheus to be seen .
There was an altar for Prometheus and two other Olympian gods in Athens , but according to the classical philologist Ulrich von  Wilamowitz-Moellendorff , this altar was for another deity called Promethos, who was venerated during the torchlight run ,which celebrated the god of ceramics and not the fire giver. Promethos was the patron of potters in Athens , and was associated with Hephaestus and Athena. He was the one who would have helped Zeus by splitting his skull to give birth to Athena , and would have shaped Pandora before creating human beings (under the supervision of Zeus).He didn’t steal fire and he was not punished.

A second Prometheus did the trickery and the stealing and was punished. He is the Prometheus mentioned by Hesiod and Aeschylus , and his name later on prevailed. All the preceding arguments are proof that people in Antiquity knew Prometheus didn’t have greatness or historical importance , and that he didn’t help or benefit anybody by his theft of fire. It seems these facts and observations were overlooked by the romantic writers and the philosophers or artists who praised Prometheus in the 19th century.
By the way , the  person or deity for whom the greatest and biggest temples and monuments were built in
Antiquity , including a statue which was one of the seven wonders of the Ancient World , was  Zeus/Jupiter.

The ‘fire’ stolen by Prometheus from the gods was most probably ordinary fire , but if it was some important property or material or discovery belonging to Zeus and to the ‘gods’ there is not much difference in the story.
In his book Les Mémoires de Zeus (The Memoirs of Zeus) , Maurice Druon gives an explanation of what might have happened. Prometheus tried to trick Zeus before stealing the fire , and Zeus decided to punish the mortal humans by taking away fire from them , but he intended to give back fire to the humans after a few months .

In any case Prometheus didn’t want to wait for Zeus to give back fire to humans , he was jealous of the power and abilities of Zeus and tried to trick him in order to hurt him or dethrone him and make him look bad , and there is no proof or mention, especially in the writings of the original ancient authors such as Hesiod , that after he stole fire he used it in a creative , beneficial or useful way for him or for the humans around him; the only ‘quality’ of the titan Prometheus mentioned by Hesiod through the theft of fire was trickery .
Even the  play Prometheus Bound by Aeschylus was misinterpreted , since the author (if it really was Aeschylus ,who showed great praise , respect and admiration for Zeus in his other plays) was using irony, and as he made Prometheus talk in the play  he intended to show him as conceited and delusional .
Prometheus could have very well played with the fire he stole (along with a number of other humans who were around him) with no useful or creative result , and after some time he let that fire die away.
What added to the confusion and misunderstanding is that the detailed facts and the sequence of events related to the theft of fire , to what happened afterwards , and to the so-called Titanomachy or war with the Titans were lost with time and are not well known .

The play Prometheus Bound was most probably written by Aeschylus ca. 415 BC (probably even earlier) . It is interesting to note that at that period of time , poets and philosophers were writing works praising and honoring Zeus.
Cleanthes ( c. 330 BC – c. 230 BC) , Stoic philosopher and the successor to Zeno as the second head (scholarch) of the Stoic school in Athens ,wrote a hymn to Zeus .The largest surviving fragment of Cleanthes is the portion of the Hymn to Zeus, in which he declares praise and honour of Zeus to be the highest privilege of all rational beings.
Callimachus (310/305–240 BC) was a noted poet, critic and scholar at the Library of Alexandria and enjoyed the patronage of the Egyptian–Greek Pharaohs Ptolemy II Philadelphus and Ptolemy III Euergetes . He also wrote a hymn to Zeus.
So it is improbable that at that time Aeschylus , who in all his other plays praised and extolled Zeus , could have written one play to damage and disparage the king of the gods. His  play about Prometheus was filled with irony and enveloped in irony.

For many centuries after the beginning of Christianity, and until the end of the eighteenth century, writers did not have a high opinion of Prometheus. The interest in Prometheus in the seventeenth century was from philosophers. 
Thomas Hobbes  saw the Titan as the reprovable example of political rebellion and democracy ( Hobbes thought the only pure and true source of power was monarchy).

A number of writers in the nineteenth century as well as in the twentieth thought that the Fathers of the Church made a parallel between Jesus Christ and Prometheus. In fact the Church Fathers (among them Tertullian) warned against establishing any kind of parallel between Prometheus and Jesus Christ, and described Prometheus as some sort of impostor when compared to God.

Some writers or authors tried to find or make comparisons and similarities between Hephaestus and Jesus Christ , or between Hercules and Jesus , etc. These comparisons (especially the one involving Prometheus) are far from accurate. 
Sometimes Prometheus has been compared to the character Loki in Norse mythology.Perhaps in Antiquity there was a common origin to Norse , Greek and similar mythologies which made them have some common characteristics, but it seems that Loki has been generally considered to be a bad trickster and a bad character , whereas Prometheus has been considered as a good trickster figure , this being the result of arbitrary unverified conjectures and interpretations , especially in the last two centuries.

The word Lucifer has been interpreted in different ways by different people , religions and cultures. When it was given the meaning of  ‘shining one’ , ‘morning star’ , or ‘light bringing’ , Prometheus , having stolen fire and apparently brought light, has been sometimes compared to Lucifer , adding to the unclear and contradictory comparisons made about him. Anyway if Prometheus is Lucifer , who is usually considered to be Satan or the Devil , then in this case Prometheus would have rebelled against Zeus ,who would be no other than God. So this whole unconvincing comparison is not profitable to Prometheus and does not show him in a good light.

The theory or conjecture stating that Zeus punished Prometheus hastily while he was still a new inexperienced ruler , and then with time became wiser and more just , doesn’t hold water.
First of all ,there’s a big difference if we consider that the death of Zeus’s father and the theft of fire took place at the end of the Titanomachy or at the beginning of this war (which was  won by Zeus). If the theft of fire took place after the death of Cronus and at the start of the conflict with the Titans , then this theft was an integral part of the conflict , and the punishment of Prometheus came as one of the results of winning this struggle. Zeus/Jupiter must have taken his time to try to reason with Prometheus and his father and brothers (to no avail), and he tried to observe (for a number of years during the conflict with the Titans) what Prometheus was doing with the thing he had stolen.
He must have noticed that Prometheus was playing carelessly with what he had stolen ; if it was fire which was
stolen , Prometheus probably kept it somewhere hidden in his house , making usage of it in rudimentary uninventive ways with no creative or useful results , and when some people he knew came to his house he showed them that fire and played , danced or frolicked with them around it.
Prometheus wasn’t at all interested in benefiting humans or in innovative technology ; it’s also possible that he could have obtained that fire by other means if he wanted , and humans possibly had basic or elementary  ways to make fire. These humans could have represented all existing humans , or they probably were a local group of humans living in the vicinity of Prometheus , Zeus , and their relatives.
In any case, Prometheus was envious of Zeus because he was the one who could make a really resourceful and innovative usage of fire , and by stealing fire he was trying to hurt Zeus.
If Zeus had seen that there was a good reason for or a beneficial purpose resulting from what Prometheus had done, or that there were attenuating circumstances in favor of the theft done by Prometheus , he (Zeus) would have been the first one to acknowledge it. But he must have found none.

There are two versions of what happened to the father of Zeus after he was defeated. One version says that after defeating his father , Zeus sent him to Tatarus or killed him.
Another version states that Cronus had bad and good traits, but his good qualities outnumbered his bad traits ,
and after Zeus helped his siblings, stood against his father and defeated him (it is best to assume this took place at the beginning of the war with the Titans) , he was reconciled with him and sent him to rule the Isles of the Blessed . Zeus surpassed his father and went beyond the abilities of his father . At the same time he  must have taken or inherited the good qualities that his father had (and also inherited good qualities from his mother), which helped him become a good and just ruler afterwards. This version of the facts is more plausible than the first one.
On the other hand , Iapetus (the father of Prometheus) had more bad traits than good ones (arrogance, limited capabilities, haughtiness) ; he was defeated by Zeus and ‘ sent to Tartarus’ at the end of the war with the Titans. Prometheus could not go beyond the potentialities of Iapetus , he stayed in the shadow of his father , and followed the old traditional narrow-minded ways of the Titans ; he had his father’s bad traits and was punished with his brothers and father by Zeus .

Not all Titans were bad or were ‘sent to Tartarus’ by Zeus. Some Titans were good , but Prometheus was not one of the good Titans  .
An example of a good (or not so bad) Titan (or Titaness) is the mother of Zeus , Rhea , and also Leto/Latona , who gave Zeus two important children: Apollo and Artemis/Diana.

When the circumstances changed and  the time was right ,  Herakles/Hercules freed and rescued Prometheus . Hercules did not do it in spite of his father Zeus , but according to his will and to his instructions . As Hesiod stated in the Theogony ,  Zeus wanted to give his son more  glory by letting him free Prometheus .
It can be rightly said that when Zeus punished Prometheus it was justice , and when he released him it was (also) justice.

In addition to books (concerning ancient mythology and religion)  I have read and mentioned in my page about religion related books  , here are some more reference works related to this post:

Divine Commerce: Near Eastern Influence on Greek Mythology , by John Kaessner.

 A Zeus wronged by Prometheus and an Aeschylus wronged by the critics. The Compassion of Orthodoxy: The Prometheus Bound of Aeschylus , by Robert L. Houbeck, Jr.
This article contains one of the best analyses I have read about the story and punishment of Prometheus.

 From Myth to Symbol. The Nineteenth-Century Interpretations of Prometheus , by Caroline Corbeau .


This topic is to be continued in another post.

 

Question: what is the square root of 36 ? – Part Two

I will continue with answers and results equal to the square root of 36 ( originally answered at quora.com ). This time the results are mostly related to physics.

With physics one has to take into account the units and the corresponding dimensions of the equations and of the constants.

6 and the square root of 36 are dimentionless numbers , so the result must be dimentionless .
If the result is a simple fraction with numerator and denominator , then the units usually cancel out.
In other cases when one deals with logarithms one should multiply with the inverse dimensions to get a dimentionless result.
In one or two results where I didn’t look for the inverse units  I multiplied the equation with a quantity I called (U) ,  which represents the inverse of the units by which one should multiply the result to get a dimentionless number.

Here are the results :

square root of 36 physics

 

One possible way to explain what I have done here is the following:
If some people , living on an isolated fictitious island or on an another hypothetical planet , attached a great importance to and had a fixation on  the square root of 36 (or the number 6) for one reason or another , and got accustomed to the use of 6 as a fundamental constant ,  unit or number , then they would have likely  tried to construct a system of measurement  based on the number 6 , and  to express physics and math formulas ,equations , constants and rules in relation to 6.

After all , 6 or \sqrt{36} is equal to :

  • The floor of  2 \pi :
    2 \pi \approx 6.2831853071795864769 ;6=\lfloor 2 \pi \rfloor
  • \frac{1}{60} of the circumference of a circle in degrees.
  • It is also  one tenth of 60 seconds which make up a minute , one tenth of 60 minutes which make up an hour , one fourth of 24 hours which equal a day on Earth , one half of  12 months which make up a year , etc.
  • A peculiar ‘hexacentric’ system , so to speak.

Or this can be seen as a (creative) exploration of or exercise in advanced math and physics in order to express many equations , formulas and constants in relation to the number 6 (or \sqrt{36} ) .
Or whatever.

Apologies to Isaac Newton , Leonhard Euler , Bernhard Riemann , Einstein , Stokes , Coulomb , Avogadro , Lagrange , and others (wherever they may be) , for playing around with their equations , formulas , constants , and/or functions.

And one more addiction to this answer :

Does the future of humanity depend on answering what is the square root of  36 , or not?
Have philosophers from Antiquity to the present overlooked this fundamental question , which goes beyond the Kantian categories of space and time set out in his Critique of Pure Reason , and beyond Nietzsche’s Beyond Good and Evil , ushering the transmutation of all values and a defining moment for a new era  in the history of Humankind?
It’s just a square root , for common sense’s sake (or is it?).

Anyway , enough philosophizing.

Here are ( 3=\frac{\sqrt{36}}{2} ) more answers to \sqrt{36} , this time with images :

\sqrt{36}  is equal to :


The number subjected to a geometric rotation in the following image (done with Mathematica and some Photoshop) :

number 6 rotated

The number expressing the power and the coefficients in the equation of the curve in the polar plot below :

number 6 polar plot

The number expressing the degree of the root  and the power of the variables in the 3D plot below :

sinc number 6

The rotated number  and the polar plotted curve in the first two images  above seem to exhibit symmetry.
Symmetry is an very important property in science , math , physics , equations , nature , and wherever it is found.

Online sources and reference works related to what I have written in this answer can be found in my pages about Science books problem solvers and philosophy books in this site/blog.

Some other online sources:
http://mathworld.wolfram.com/

http://en.wikipedia.org/wiki/Category:Mathematics

http://en.wikipedia.org/wiki/Category:Physics

About me and comics, comic books, and movies

This is a website and blog about culture , science , and related subjects , and it is supposed to be a serious website . But then again , as one famous jester and villain said :”Why so serious?”

Comics and comic books ( and movies ) are nowadays part of general and popular culture , and they have a place in this blog , given also the fact that I’ve been reading comic books ( and watching movies about them ) for many years.

I started reading comic books when I was a little kid.I read them in Arabic , in French and in English.
I read comics by DC Comics (Superman , Batman , the Flash ,and others) and Marvel Comics (Spiderman ,Fantastic Four ,Thor , and others) .Maybe I read a little more DC than Marvel Comics , but I read both , and I also read other types of comics.One series of comic books I bought and read years ago was about The Death and Return of Superman.
I also read a number of Franco-Belgian comic books , especially the Adventures of Tintin , and Asterix and Obelix.

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From a sociological point of view , comics and comic books reflect in general the beliefs , customs , conventions and accepted ideas of the society which produced them , as well as the sociopolitical milieu and period in which they were created.
Some comics about historical events, historical figures or adventures taking place in the past may be enjoyable but may also be fanciful and inaccurate (which can also be true of a number of historical novels).

Comic books such as those by DC and Marvel Comics display a good amount of facts related to or borrowed from science and physics.Sometimes these comics present stories and fiction with scientific insights and interesting information about physics , astrophysics ,chemistry and the exact sciences , but these stories also contain what could be called ‘technobabble’ , things and statements revolving around science but imprecise , unrealistic or unexplainable according to the known laws and rules of physics.At times the reader has to allow for exceptions to existing scientific and physical laws in order to continue reading the fictional tales presented to him.

One relationship or pairing I liked in DC Comics is the following:

Superman and Wonder woman

Some may prefer Superman staying with Lois Lane and marrying her , others like this new relationship and even imagine Superman and Wonder Woman getting married or having kids  . I think one possible  way to resolve the issue would be  to connect two storylines .In the movie ‘Superman Returns‘ , Superman had a son with Lois Lane , so if this fact could be used as an ending to the relationship between Lois and Clark , and the beginning of the relation between Diana and Clark considered as a continuation of that storyline , then this could be satisfactory for all fans and readers , and  the affair between the Son of Krypton and The Amazon Princess can go on to its completion.

Concerning one particular aspect of fictional science in comic books and movies ,and based on my own readings and analysis of scientific rules and facts , I think that although time travel is an interesting  idea or concept , it is  not possible and will not happen in reality. Perhaps I will write more about this subject in the future.

The Adventures of Tintin are all entertaining ,with two comic books in the series (Destination Moon and Explorers on the Moon) anticipating the first human trip to the Moon before it actually happened.It was a good piece of science fiction , although it contained a few errors.One book in the series , Vol 714 Pour Sydney or Flight 714 , which dealt with the existence of UFOs and Extraterrestrials , was in my opinion scientifically unverifiable and somewhat unrealistic.

Other Franco-Belgian comics I have read include :
Gaston Lagaffe , Spirou and Fantasio , Barbe Rouge , Iznogood , Ric hochet , Lucky Luke , Les Tuniques Bleus , Chick Bill , Les Schtroumpfs (the Smurfs) , Benoît Brisefer , Johan et Pirlouit (Johan and Peewit) , Alix , Les Petits Hommes …

Additional reference work related to this post:
The Physics of Superheroes : Spectacular Second Edition , by James Kakalios.

Calendars ,days of the week , and dates

There are different calendar systems that are still used or were used in the past . Examples include the Julian calendar , the Gregorian calendar , the Hebrew calendar , the Islamic and the Iranian calendars , the French Republican calendar , etc. Most calendars use astronomical events and cycles as their basis: the day is based on the rotation of planet Earth on its axis , the month is based on the Moon revolving around the Earth , and the year is based on the period of revolution of the Earth around the Sun.The influence of the gravitational force from other planets may cause the length of a particular year to vary by several minutes. The Gregorian calendar was introduced in 1582 .Dates before October 1582 are usually given in the Julian calendar .

Here is a list of leap years in the Gregorian calendar from 2016 to 2416 (done with the help of Mathematica) :

2016 , 2020 , 2024 , 2028 , 2032 , 2036 , 2040 , 2044 , 2048 , 2052 , 2056 , 2060 , 2064 , 2068 , 2072 , 2076 , 2080 , 2084 , 2088 , 2092 , 2096 , 2104 , 2108 , 2112 , 2116 , 2120 , 2124 , 2128 , 2132 , 2136 , 2140 , 2144 , 2148 , 2152 , 2156 , 2160 , 2164 , 2168 , 2172 , 2176 , 2180 , 2184 , 2188 , 2192 , 2196 , 2204 , 2208 , 2212 , 2216 , 2220 , 2224 , 2228 , 2232 , 2236 , 2240 , 2244 , 2248 , 2252 , 2256 , 2260 , 2264 , 2268 , 2272 , 2276 , 2280 , 2284 , 2288 , 2292 , 2296 , 2304 , 2308 , 2312 , 2316 , 2320 , 2324 , 2328 , 2332 , 2336 , 2340 , 2344 , 2348 , 2352 , 2356 , 2360 , 2364 , 2368 , 2372 , 2376 , 2380 , 2384 , 2388 , 2392 , 2396 , 2400 , 2404 , 2408 , 2412 , 2416 .

In the Gregorian calendar , most years that are multiples of 4 are leap years . The years 2100, 2200, 2300 are not leap years .

Below is a list of the days of the week each one corresponding to the first day of the year (Gregorian calendar) from the year  2016 to 2036 :

  • 1/1/2016 : Friday.
  • 1/1/2017 : Sunday.
  • 1/1/2018 :Monday.
  • 1/1/2019: Tuesday.
  • 1/1/2020: Wednesday.
  • 1/1/2021: Friday.
  • 1/1/2022: Saturday.
  • 1/1/2023: Sunday.
  • 1/1/2024: Monday.
  • 1/1/2025: Wednesday.
  • 1/1/2026: Thursday.
  • 1/1/2027: Friday.
  • 1/1/2028: Saturday.
  • 1/1/2029: Monday.
  • 1/1/2030: Tuesday.
  • 1/1/2031: Wednesday.
  • 1/1/2032: Thursday.
  • 1/1/2033: Saturday.
  • 1/1/2034: Sunday.
  • 1/1/2035: Monday.
  • 1/1/2036: Tuesday.

Next I give the day of the week corresponding to the 4th of July from the year 2015 to 2020:

  • 2015: 4th of July is a Saturday.
  • 2016: 4th of July is a Monday.
  • 2017: Tuesday.
  • 2018: Wednesday.
  • 2019: Thursday.
  • 2020: Saturday.

The day of the week corresponding to the 14th of July (Bastille day in France) from the year 2015 to 2020:

  • 2015: 14th of July is a Tuesday.
  • 2016: Thursday.
  • 2017: Friday.
  • 2018: Saturday.
  • 2019: Sunday.
  • 2020: Tuesday.

Easter Sunday date (Western churches and Greek Orthodox churches) for 4 years:

  • 27 March 2016 (Western), 1 May 2016 (Greek Orthodox).
  • 16 April 2017 , same date for Greek Orthodox churches.
  • 1 April 2018 , 8 April 2018.
  • 21 April 2019 , 28 April 2019.

Here are days of the week corresponding to some important historical dates and people (after 1582 the dates are in the Gregorian calendar) :

  • The most accepted date for the Death of Genghis Khan  ( Julian calendar) is 18 August 1227 , which was a Wednesday.The date in the Gregorian calendar would be  Wednesday 25 August 1227.
  • Columbus reached America : Friday 10 October 1492 (Julian calendar). The date in the Gregorian calendar would be Friday 21 October 1492.
  • First publication of Philosophiæ Naturalis Principia Mathematica by Isaac Newton: Saturday 5 July 1687 ( Gregorian).
  • Date of birth of Carl Friedrich Gauss : Wednesday 30 April 1777.
  • Date of death of Carl Friedrich Gauss: Friday 23 February 1855.
  • Death of Napoleon Bonaparte : Saturday 5 May 1821.
  • Date of birth of Jules Verne : Friday 8 February 1828.
  • Date of birth of Pierre Simon Laplace : Wednesday 23 April 1749.
  • Death of Pierre Simon Laplace : Thursday 5 April 1827.

Another day of the week and date: Sunday , 31 July 2072 (this date is somewhat important for me).

The Islamic calendar is a lunar calendar ( based on the motion and phases of the Moon) of 12 months  with alternating months of 29 and 30 days , and  a year made of 354 days , which is about 11 days shorter than the length of the year in the Gregorian calendar. In the table below I give the day of the week corresponding to the first day of the year (Islamic calendar) and the corresponding Gregorian date for a number of consecutive years:

Year(Islamic calendar) First day of the year Gregorian date
1/1/1437  Thursday  15 October 2015
1/1/1438  Monday  3 October 2016
 1439  Friday  22 September 2017
 1440  Wednesday  12 September 2018
 1441  Sunday  1 September 2019
 1442  Thursday  20 August 2020
 1443  Tuesday  10 August 2021
 1444  Saturday  30 July 2022
 1445  Wednesday  19 July 2023
 1446  Monday  8 July 2024
 1447  Friday  27 June 2025
 1448  Wednesday  17 June 2026
 1449  Sunday  6 June 2027
 1450  Thursday  25 May 2028
 1451  Tuesday  15 May 2029
 1452  Saturday  4 May 2030
 1453  Wednesday  23 April 2031
 1454  Monday  12 April 2032
 1455  Friday  1 April 2033
 1456  Tuesday  21 March 2034
1457 Sunday 11 March 2035
1458 Thursday 28 February 2036
1459 Tuesday 17 February 2037
1460 Saturday 6 February 2038
1461 Wednesday 26 January 2039
1462 Monday 16 January 2040
1463 Friday 4 January 2041
1464 Tuesday 24 December 2041
1465 Sunday 14 December 2042
1466 Thursday 3 December 2043
1467 Tuesday 22 November 2044

A good online calendar converter can be found in here.

A number of scholars , thinkers and scientists in the past  have written books and studies about calendars , the chronology of world history and historical events (such as Isaac Newton’s The Chronology of Ancient Kingdoms and al Biruni‘s The Chronology of Ancient Nations , also known as The Remaining Signs of Past Centuries).

Newton Chronology of ancient kingdoms

However , historical chronology and dates before the beginning of the Christian Era are mostly approximate , uncertain or imprecise. Therefore I think a better and more accurate chronology of ancient History (and of World History in general) ought to be constructed , using rigorous historiographical and historical methods , and unbiased scientific reasoning , analysis , and methods.