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Category: the true

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The Future of Fundamental Physics : Nima Arkani-Hamed

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The Treasury of Knowledge : Book Six Parts One and Two

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Cohl Furey – summary – links between the Standard Model of particle physics and the octonions

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Money as a System-of-Control – Andreas M. Antonopoulos

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Plutarch on Empedocles

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John Archibald Wheeler : Information, Physics, Quantum : The Search for Links

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Carlo Rovelli – “Space is blue and birds fly through it”

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IBM 50 qubit system

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Israeli Practices towards the Palestinian People

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Evolution of Hindu-Arabic numerals

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place of origin all of the characters in Homer’s Iliad

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Standard Model of particle physics written in the Lagrangian

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Euclid

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Edward Witten : Magic, Mystery, and Matrix

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John Dee

In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold {\displaystyle \mathbb {O} } \mathbb {O} . Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative.

Octonions are not as well known as the quaternions and complex numbers, which are much more widely studied and used. Despite this, they have some interesting properties and are related to a number of exceptional structures in mathematics, among them the exceptional Lie groups. Additionally, octonions have applications in fields such as string theory, special relativity, and quantum logic. [ wikipedia ]

by Carlo Rovelli – “Quantum mechanics is not about ‘quantum states’: it is about values of physical variables. I give a short fresh presentation and update on the relational perspective on the theory, and a comment on its philosophical implications.” (Submitted on 8 Dec 2017 (v1), last revised 29 Jan 2018 (this version, v5))

Israeli Practices towards the Palestinian People and the Question of Apartheid – Palestine and the Israeli Occupation , Issue No. 1 United Nations Beirut, 2017

Rima Khalaf, the head of the Economic and Social Commission for Western Asia (ESCWA) which published the report, announced her resignation at a press conference in Beirut on Friday.

Reuters reports that Khalaf took the step “after what she described as pressure from the secretary-general to withdraw a report accusing Israel of imposing an ‘apartheid regime’ on Palestinians.”

“I resigned because it is my duty not to conceal a clear crime, and I stand by all the conclusions of the report,” Khalaf stated. | see also

By Pinpin [GFDL or CC BY-SA 3.0], via Wikimedia Commons

Section 1

These three lines in the Standard Model are ultraspecific to the gluon, the boson that carries the strong force. Gluons come in eight types, interact among themselves and have what’s called a color charge.

Section 2

Almost half of this equation is dedicated to explaining interactions between bosons, particularly W and Z bosons.

Bosons are force-carrying particles, and there are four species of bosons that interact with other particles using three fundamental forces. Photons carry electromagnetism, gluons carry the strong force and W and Z bosons carry the weak force. The most recently discovered boson, the Higgs boson, is a bit different; its interactions appear in the next part of the equation.

Section 3

This part of the equation describes how elementary matter particles interact with the weak force. According to this formulation, matter particles come in three generations, each with different masses. The weak force helps massive matter particles decay into less massive matter particles.

This section also includes basic interactions with the Higgs field, from which some elementary particles receive their mass.

Intriguingly, this part of the equation makes an assumption that contradicts discoveries made by physicists in recent years. It incorrectly assumes that particles called neutrinos have no mass.

Section 4

In quantum mechanics, there is no single path or trajectory a particle can take, which means that sometimes redundancies appear in this type of mathematical formulation. To clean up these redundancies, theorists use virtual particles they call ghosts.

This part of the equation describes how matter particles interact with Higgs ghosts, virtual artifacts from the Higgs field.

Section 5

This last part of the equation includes more ghosts. These ones are called Faddeev-Popov ghosts, and they cancel out redundancies that occur in interactions through the weak force.

Thomas Gutierrez, an assistant professor of Physics at California Polytechnic State University, transcribed the Standard Model Lagrangian for the web. He derived it from Diagrammatica, a theoretical physics reference written by Nobel Laureate Martinus Veltman. In Gutierrez’s dissemination of the transcript, he noted a sign error he made somewhere in the equation.

in Symmetry

One of the oldest [ca. 75-125 A.D] and most complete diagrams from Euclid’s Elements of Geometry is a fragment of papyrus found among the remarkable rubbish piles of Oxyrhynchus in 1896-97 by the renowned expedition of B. P. Grenfell and A. S. Hunt. It is now located at the University of Pennsylvania. The diagram accompanies Proposition 5 of Book II of the Elements, and along with other results in Book II it can be interpreted in modern terms as a geometric formulation of an algebraic identity – in this case, that ab + (a-b)2/4 = (a+b)2/4

“If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half.” (from the classic translation of T. L. Heath)

“Quantum field theory is a very rich subject for mathematics as well as physics. But its development in the last seventy years has been mainly by physicists, and it is still largely out of reach as a rigorous mathematical theory despite important efforts in constructive field theory. So most of its impact on mathematics has not yet been felt. Yet in many active areas of mathematics, problems are studied that actually have their most natural setting in quantum field theory. Examples include Donaldson theory of four-manifolds, the Jones polynomial of knots and its generalizations, mirror symmetry of complex manifolds, elliptic cohomology, and many aspects of the study of affine Lie algebras.

To a certain extent these problems are studied piecemeal, with difficulty in understanding the relations among them, because their natural home in quantum field theory is not now part of the mathematical theory. To make a rough analogy (Figure1), one has here a vast mountain range, most of which is still covered with fog. Only the loftiest peaks, which reach above the clouds, are seen in the mathematical theories of today, and these splendid peaks are studied in isolation, because above the clouds they are isolated from one another. Still lost in the mist is the body of the range, with its quantum field theory bedrock and the great bulk of the mathematical treasures.”

this is most lovely….