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Recent Posts
 Luigi Luca CavalliSforza
 Frank Wilczek corrects a misunderstanding
 Fractional Spin
 Chris Quigg’s Summary of the Evolution of Particle Physics
 Free version of the Feynman Lectures on Physics
 Huge amount of water in Earth’s mantle (2)
 Final reports from the Planck Cosmic Microwave Background Measurements
 The Centennial of Julian Schwinger
 Where were we?
 Fog
 Carmel
 Causal emergence, downward causation, and more…
 Few comments on the pratityasamutpada concept
 Word clouds
 Etymology of elementary particle names
 On the concept of scalar field
 Is there a particle that interacts with muons but not electrons?
 Updated links: LHC (Large Hadron Collider) operation
 Testing Google Neural Machine Translation (Turkish to English)
 Ernst Mach
 A rare good news from Middle East: SESAME opens
 China’s Noah’s Ark
 Polyakov classic: Confinement and Liberation
 1933 New Yorker articles on Einstein
 Muon g2 mystery
 Most watched physics videos (compiled by TrueSciPhi)
 Story of how Feynman tried to get rid of fields but couldn’t
 Form
 2017 Oppenheimer Lecture by John Preskill on Quantum Computing
 You know, it would be sufficient to really understand the electron
 How long does it take to reach the bottom?
 Primordial qubit network perspective
 On the photonphoton interaction
 The Legacy of the Tevatron by S.D. Holmes and V.D. Shiltsev
 In 4 space dimensions all knots can be unraveled
 Stanford
 A profile of Roger Penrose by Philip Ball
 Updates (February 2017)
 Sounds of Aya Sophia
 EDGE 2017 question and 206 responses by invited contributors
 Update on how Earth’s magnetic field is changing
 John Hagelin’s “Restructuring Physics” article from 1989
 Updates (December 2016)
 Reflections on this anniversary of Shebi Arus (2016)
 Cartoon guide to quantum computing by Scott Aaronson and Zach Weinersmith
 Qubit
 Book bunker below Bryant Park
 Unsolved problems in physics
 Nobel Prizes for Accelerator/Beam Physics
 A guide to Richard Gauthier’s Electron Models
 Knowledgebase
 Updates (November 2016)
 L.V. Lorenz and H.A. Lorentz
 Edward Witten’s 2014 Kyoto Prize commemorative lecture
 Geometrical versus Topological
 Super performance of the Large Hadron Collider in 2016
 Fourth type of neutrino has never been observed
 Guest Post by Raymond Bates on Panpsychism
 Few comments on Horgan’s bunkbashing diatribe
 Roger Penrose’s latest book: Fashion, Faith, and Fantasy
 Atiyah lecture at 2016 Heidelberg Laureate Forum
 Matthew Buckley’s particle physics tutorial articles at Boston Review
 Epistemic uncertainty
 CASW Showcase interview with Natalie Wolchover
 bioRxiv: the preprint server for Biology
 Can astronauts see the stars by the naked eye in space?
 LMFDB: unifying the building blocks of mathematics
 Tanedo on the 17 MeV Anomaly in Beryllium Nuclear Decays
 A lot is happening
 Large Hadron Collider (LHC) is breaking performance records
 FERMILAB History and Archives Project
 Helen Thom Edwards
 The 500 article milestone: time for reflection
 Galileo’s Diagramma Della Verita
 Curious about lunar calendars
 How long astronauts stayed on the moon?
 Subspace
 Lost in translation (3)
 Counterfactual definiteness
 Updates (May 2016)
 Pioneers of Microvita Research (3): HansJoachim Rudolph
 Pioneers of Microvita Research (2): Frank van den Bovenkamp
 Pioneers of Microvita Research (1): Richard Gauthier
 Microvita links
 Lost in translation (2)
 What is an inverse femtobarn?
 Live Beam Status at LHC
 EDGE 2016 question and 198 responses by the invited contributors
 A short comment on Reichenbach’s Principle of Common Cause
 Sad state of physics education in Turkey
 Updates (April 2016)
 Interesting karma between Einstein and Bohr
 Updates (March 2016)
 Payback
 alla turca time
 Smell of space
 Quick reminders about the leap day
 Umberto Eco
 Principle of minimal structure
 Direct observation of gravitational waves by the Advanced LIGO
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Category Archives: mathematics
A profile of Roger Penrose by Philip Ball
I have mentioned several times in this blog that Roger Penrose is one of my three heroes in physics – others being Albert Einstein and Gerard ‘t Hooft. The UK magazine Prospect published a profile of Roger Penrose. I enjoyed this … Continue reading
Posted in mathematics, philosophy, physics
Tagged Roger Penrose
Geometrical versus Topological
NYC geographical map shown below is an example of geometrical representation. The distances between the boroughs of NYC are proportional to the actual distances. NYC subway diagram shown below is an example of topological representation. On this topological map the distances between the boroughs … Continue reading
Posted in mathematics
Tagged Geometry, graph theory, mathematics, topology
Atiyah lecture at 2016 Heidelberg Laureate Forum
Image credit Before you watch Atiyah’s wonderful lecture given at the Heidelberg Laureate Forum you should first read these two blogpost by Ben Orlin: 21 Essential Quotes from Sir Michael Atiyah interview (Quanta Magazine): Michael Atiyah’s Imaginative State of Mind … Continue reading
Posted in mathematics
Tagged Heidelberg Laureate Forum
LMFDB: unifying the building blocks of mathematics
image credit: http://www.lmfdb.org The LMFDB is a new web resource developed by a large team of mathematicians around the world. The www.lmfdb.org describes LMFDB as the database of Lfunctions, modular forms, and related objects. Lfunctions are like the DNA of mathematics. The article … Continue reading
Posted in mathematics
Tagged computational number theory, Lfunctions, modular forms
Centennial Anniversary of Einstein’s General Relativity Theory
100 years a ago on November 25 1915 Albert Einstein presented the final version of his theory of gravitation known as the General Relativity to Prussian Academy of Sciences. The paper was published in 1916. Why do we mention David Hilbert in the … Continue reading
Polchinski’s review paper: Dualities of Fields and Strings
I have read Joseph Polchinski’s excellent review paper titled “Dualities of Fields and Strings“. This paper is written for experts. I am not an expert in fields and strings. I am not an expert in dualities either but I was able … Continue reading
Posted in mathematics, physics
Tagged physics dualities
Cubic curves
The reason I am interested in cubic curves is that they may be the simplest mathematical representations of the twisting action. In “Prometheus and Chronos” I tried to build a conceptual model of particles based on the hypothesis of intrinsic … Continue reading
Posted in computer science, geometry, mathematics, physics
Tagged cubic curves, elliptic curves
AlBiruni
image credit I feel so ashamed for not knowing much about alBiruni – the polymath who lived in the 11’th century. His name was brought to my attention by a newspaper article announcing the establishment of a new private university … Continue reading
Posted in geometry, geophysics, history, inspiration, linguistics, mathematics, philosophy, physics, Turkish
Tagged alBiruni, Indology, mathematics, physics, polymath
Maryam Mirzakhani: the first woman to win a Fields Medal
Image credit Maryam Mirzakhani — a 37yearold mathematics professor at Stanford University — was awarded a Fields Medal. She is the first woman to win a Fields Medal – the most prestigious prize in mathematics. The Fields Medal is awarded every four … Continue reading
Posted in mathematics
Tagged hyperbolic surfaces, Iranian mathematicians, mathematics
Credence
I saw the word “credence” in a blog post by Sean Carroll. He defines credence as “degree of belief.” Here’s an interesting quote from that blog post “Quantum probabilities are really credences — statements about the best degree of belief … Continue reading
Posted in mathematics, philosophy, physics
Tagged Bayesian statistics, degree of belief, degree of confidence, philosophy, physics, Probability, Statistics
A selection of resources on mathematics, physics and philosophy
In my previous post I mentioned the existence of a “collective mechanism” that pays attention to improvements/innovations in individual expressions. I try to do my part and bring the reader’s attention to excellent educational resources on math, physics and philosophy. I … Continue reading
Posted in mathematics, philosophy, physics
Tagged Education, encyclopedia, mathematics, philosophy, physics, resources, tutorials
Angle
An angle is always defined by 2 numbers Typically those 2 numbers are related to 2 line segments that have a common end point. The coordinate system or the nature of the space in which these line segments are embedded … Continue reading
Posted in mathematics, science
Tagged angle, Geometry, phase
π Day
March 14 is the day. Coincidentally, March 14 is also the birthday of Albert Einstein. The best encyclopedic resource for anything related to mathematics is Wolfram MathWorld which is created, developed and nurtured by Eric Weisstein. I have tremendous respect … Continue reading
Posted in mathematics, society, tutorial
Atiyah’s Grand Survey of Duality in Mathematics and Physics
Michael Francis Atiyah, OM, FRS, FRSE, FAA is a British mathematician specializing in geometry. He was awarded the Fields Medal in 1966, the Copley Medal in 1988, and the Abel Prize in 2004. Michael Atiyah was a professor at both … Continue reading
Posted in mathematics
Tagged algebra, Algebraic Geometry, Cambridge, Duality (mathematics), Duality (physics), Geometry, Michael Atiyah, Oxford, topology
Einstein and Gödel
When I was younger I was deeply impressed by Douglas R. Hofstadter’s book “Gödel, Escher, Bach: An Eternal Golden Braid.” The “Gödel” in the title of that book refers to Kurt Gödel who was one of the greatest mathematicians of … Continue reading
Posted in history, mathematics, physics
Tagged Einstein, Kurt Godel
Quanta Magazine (Simons Foundation)
The Quanta Magazine is a new scientific magazine published online by an editorially independent division of the Simons Foundation. You can reach the magazine at: https://www.simonsfoundation.org/quanta/ “Quanta Magazine is an online publication whose mission is to enhance public understanding of … Continue reading
Posted in geometry, mathematics, physics, science
Tagged Math, Quanta Magazine, Simons Foundation
Few Comments on the Pair Concept
In my previous post I mentioned that Complex number can be thought of as a pair of real numbers. Quaternion can be thought of as a pair of complex numbers Octonion can be thought of as a pair of quaternions … Continue reading
Posted in mathematics, physics
Cayley–Dickson Construction of Complex, Quaternion and Octonion Numbers
Complex number can be thought of as a pair of real numbers. Quaternion can be thought of as a pair of complex numbers Octonion can be thought of as a pair of quaternions When we construct the complex, quaternion and … Continue reading
Posted in mathematics
Tagged Complex number, Octonion, Quaternion, Real number
Geometric Algebra (1)
Geometric algebra is not to be confused with algebraic geometry. Geometric algebra is also known as Clifford algebra which has many applications in physics and engineering. Algebraic geometry, on the other hand, is a branch of abstract mathematics. Geometric algebra … Continue reading
Posted in mathematics, tutorial
Tagged Clifford algebra, Euclidean space, Multivector
Geometric interpretation of sqrt(1)
I wrote a post titled Euler rule is almost mystical where I mentioned the CotesEuler identity Euler rule is a special case of the CotesEuler identity. represents the rotations of the complex unit vector. This provides a natural interpretation for … Continue reading
Posted in mathematics, tutorial
Tagged Complex plane, Euler's identity
Biquaternion
In the previous post we have seen that a quaternion is defined as where and , , , are real numbers. Biquaternion The biquaternion is a complexified quaternion where , , , are complex numbers. The basis elements , , … Continue reading
Quaternion
Quaternions are 4dimensional generalizations of complex numbers. It can also be said that the basis elements , , of a quaternion are 3dimensional generalization of the pure imaginary number . William Rowan Hamilton discovered quaternions in 1843. After many years … Continue reading
Posted in mathematics, tutorial
Tagged Complex number, Quaternion, William Rowan Hamilton
Mathematical Spirals
The equations of the basic spirals are given in polar coordinates. The is the radius and is the angle measured from the positive horizontal axis.The and are constants. Archimedes Spiral http://mathworld.wolfram.com/ArchimedesSpiral.html Fermat Spiral http://mathworld.wolfram.com/FermatsSpiral.html Logarithmic Spiral http://mathworld.wolfram.com/LogarithmicSpiral.html Golden Spiral The … Continue reading
Golden Number and Lucas Sequence
The golden number is . There is extensive literature on the golden number which is also known as the golden ratio. The exposition in Wolfram Mathworld [http://mathworld.wolfram.com/GoldenRatio.html] is excellent. John Baez gave an interesting exposition [http://math.ucr.edu/home/baez/week203.html]. Mario Livio’s book “The Golden … Continue reading
Posted in mathematics, tutorial
Tagged Golden Number, Golden ratio, Lucas, Math
Phase enables relativity
Physicists are experts at assigning new meanings to the terms established in common language. I mentioned the term “dual” or “duality” before. In common language dual means two. In physics dual means equivalent. Physicists use the word “phase” in different … Continue reading
Posted in geometry, mathematics, physics, science, tutorial
Euler rule is almost mystical
In his wonderful book “Road to Reality” Roger Penrose mentions that the Euler rule is “almost mystical” because it relates the 5 fundamental numbers 0, 1, i, π and e to each other. The Euler rule is a special case … Continue reading
Posted in mathematics, tutorial
Tagged Complex number, Euler, Euler's identity
i raised to the power of i
Remember the general rule Using this rule we can compute i raised to the power of i remember that and
Posted in mathematics, tutorial
Tagged FAQs Help and Tutorials
Zero
Symbols for zero appeared in many cultures Before Common Era (BCE). The philosophical conception of zero, however, is usually attributed to the Indian philosophy. The evidence is in the Sanskrit language. The Sanskrit word “shunya” meaning “emptiness” or “void” was … Continue reading
Posted in history, mathematics, philosophy
Tagged Indian philosophy, MarcAlain Ouaknin, mathematics, Sanskrit
Super Modeler Function
Data modeling capabilities of this function is limitless. X is a continous variable. S, R, T are constants. By changing the constants see how the Super Modeler Function is behaving. In the graphs below the horizontal axis is the X … Continue reading
Posted in mathematics
Tagged mathematics, physics