Entropy (information theory) 2 bits of entropy. A single toss of a fair coin has an entropy of one bit. A series of two fair coin tosses has an entropy of two bits. The number of fair coin tosses is its entropy in bits. This random selection between two outcomes in a sequence over time, whether the outcomes are equally probable or not, is often referred to as a Bernoulli process. The entropy of such a process is given by the binary entropy function. This definition of "entropy" was introduced by Claude E. Entropy is a measure of unpredictability of information content. Now consider the example of a coin toss. English text has fairly low entropy. If a compression scheme is lossless—that is, you can always recover the entire original message by decompressing—then a compressed message has the same quantity of information as the original, but communicated in fewer characters. Shannon's theorem also implies that no lossless compression scheme can compress all messages. . The average uncertainty , with
Entropy Figure 1: In a naive analogy, energy in a physical system may be compared to water in lakes, rivers and the sea. Only the water that is above the sea level can be used to do work (e.g. propagate a turbine). Entropy represents the water contained in the sea. In classical physics, the entropy of a physical system is proportional to the quantity of energy no longer available to do physical work. History The term entropy was coined in 1865 [Cl] by the German physicist Rudolf Clausius from Greek en- = in + trope = a turning (point). The Austrian physicist Ludwig Boltzmann [B] and the American scientist Willard Gibbs [G] put entropy into the probabilistic setup of statistical mechanics (around 1875). The concept of entropy in dynamical systems was introduced by Andrei Kolmogorov [K] and made precise by Yakov Sinai [Si] in what is now known as the Kolmogorov-Sinai entropy. The formulation of Maxwell's paradox by James C. Entropy in physics Thermodynamical entropy - macroscopic approach References
8. Reductio ad Absurdum – A Concise Introduction to Logic 8.1 A historical example In his book, The Two New Sciences,[10] Galileo Galilea (1564-1642) gives several arguments meant to demonstrate that there can be no such thing as actual infinities or actual infinitesimals. One of his arguments can be reconstructed in the following way. He also proposes that we take as a premise that there is an actual infinity of the squares of the natural numbers. Now, Galileo reasons, note that these two groups (today we would call them “sets”) have the same size. If we can associate every natural number with one and only one square number, and if we can associate every square number with one and only one natural number, then these sets must be the same size. But wait a moment, Galileo says. We have reached two conclusions: the set of the natural numbers and the set of the square numbers are the same size; and, the set of the natural numbers and the set of the square numbers are not the same size. 8.2 Indirect proofs (P→(QvR)) This argument looks valid.
untitled Chapter 4: Music I preface the following by the admission that I have developed little to no musical aptitude as yet and have never studied music theory. However, that does not seem to have stopped me from uncovering what looks to be some very interesting observations having applied Mod 9 to the frequencies generated by the black and white keys of the musical scale. 1955 saw the introduction of the International Standard Tuning of 440 Hz on the A of Middle C Octave. This standardised all instruments around the world. The C's were all 3 & 6, same for C sharp, then D's are all 9's and on until I came to F which revealed the 1 2 4 8 7 5 sequence, in order. You will notice that using this tuning at 440 Hz we see that: 5 sections of the octave are 1 2 4 8 7 5 4 sections are 3 & 6 3 sections are 9 Immediately the Pythagorean 3 4 5 triangle springs to mind. Above, we can clearly see that, as with the numbers, the octaves are paired up symmetrically and reflected, separated by 3 octaves. Cymatics.
The Zero Point Field: How Thoughts Become Matter? | HuffPost Life Since I have mentioned the zero point field (ZPF) so much in my past HuffPost articles, and seeing as how it is a vital component to what is going on, it only makes sense to provide a more detailed analysis for all those Quantum buffs who struggle with my theory that thoughts equal matter. So, let's start with the basics and show what is known about the ZPF, and how its discovery come about? ZPF Basics In quantum field theory, the vacuum state is the quantum state with the lowest possible energy; it contains no physical particles, and is the energy of the ground state. This is also called the zero point energy; the energy of a system at a temperature of zero. But quantum mechanics says that, even in their ground state, all systems still maintain fluctuations and have an associated zero-point energy as a consequence of their wave-like nature. Liquid helium-4 is a great example: Under atmospheric pressure, even at absolute zero, it does not freeze solid and will remain a liquid.
The “Sound” of Weyl Fermions Binghai Yan, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel A prediction of a new heat-transport mechanism—called chiral zero sound—may explain recent observations of a “giant” thermal conductivity in Weyl semimetals. Heat in a solid is mainly carried by lattice vibrations (phonons) and conducting electrons. These mechanisms of heat conduction are so dominant over other forms that in an ordinary material they are often assumed to be the only ones that matter. A Weyl semimetal is a material that hosts particles known as Weyl fermions. Because of this intrinsic chirality, Weyl quasiparticles behave differently than electrons in ordinary metals or semiconductors. A signature of the chiral anomaly is negative magnetoresistance—a lowering of resistance with increasing magnetic field, which has been observed in Weyl materials by several groups. Sun’s team, however, observed strikingly different behavior in TaAs. References Z. About the Author Subject Areas
What is an epsilon in mathematics? How is it used? NUCLEAR GRAVITATION FIELD THEORY I served as a Naval Officer assigned to United States Navy Nuclear Fast Attack Submarine U.S.S. Flasher (SSN-613) home ported in San Diego, California, from January 1979 through June 1982. During my sea tour aboard U.S.S. Flasher (SSN-613), I served as the Electrical Officer, the Communications and Electronic Materials Officer, the Main Propulsion Assistant to the Engineer Officer, and Assistant Operations Officer. From November 1979 to June 1980, I participated in my first Western Pacific Deployment aboard U.S.S. The second half of the deployment, U.S.S. In June 1981 I completed all the requirements for Qualification in Submarines giving me the right to wear the Gold Dolphins with honor and become a member of a very elite group of people. From July 1981 to January 1982, I participated in my second Western Pacific Deployment aboard U.S.S. Upon completion of my obligated service to the United States Navy, I completed my tour aboard U.S.S.
How much does a kilogram weigh? During a seminar at CERN, Klaus von Klitzing, the 1985 Physics Nobel Laureate, explained how the definition of the kilogram will be revolutionised The National Institute of Standards and Technology (NIST)-4 Kibble balance measured Planck's constant to within 13 parts per billion in 2017, accurate enough to assist with the redefinition of the kilogram. (Image: J. The Kilogram doesn’t weigh a kilogram any more. Together with six other units – metre, second, ampere, kelvin, mole, and candela – the kilogram, a unit of mass, is part of the International System of Units (SI) that is used as a basis to express every measurable object or phenomenon in nature in numbers. To solve this weight(y) problem, scientists have been looking for a new definition of the kilogram. Planck’s constant will be assigned an exact fixed value based on the best measurements obtained worldwide. “There’s nothing to be worried about,” says Klaus von Klitzing. However, the redefinition process is not that simple.
A Level H2 Chemistry Syllabus Videos - ChemGuru Top A Level Chemistry Tutor Maverick Puah the Chemistry Guru shares his knowledge on via his video lessons. Students will find them useful for supplementing their A Level Chemistry notes and H2 Chemistry notes. These video resources follow the new syllabus (Subject Code 9729) closely. For differences from the old syllabus do check out our detailed comparison. You can also check out SEAB (Singapore Examinations and Assessment Board) website on the examination syllabuses offered for A Levels. Do check out the video lessons for the following topics that are currently available. Organic Chemistry Physical Chemistry 2017 A Level H2 Chemistry Paper 1 Solutions Subscribe to our mailing list for weekly updates! Here are the list of topics covered for A Level Chemistry Syllabus: Physical Chemistry 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Organic Chemistry 1. 2. 3. 4. 5. 6. 7. 8. 9. Inorganic Chemistry 1. 2. 3. 4.