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[[Kategorie:DZ]]
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== W2 // WISSEN2 ==
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W2 per [[Facebook]] group==
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https://www.facebook.com/groups/wissen2/
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WISSEN2 per [[AKI]]-wiki==
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http://wiki.aki-stuttgart.de
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...
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WISSEN2 ist ein modul im Blended learning & Personal training==
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...
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*Kontakt: Karl Dietz
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*karl.dz@gmail.com
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*Tel. 0172 / 768 7976
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==The 17 Equations That Changed The World==
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1) The Pythagorean Theorem : This theorem is foundational to our understanding of geometry. It describes the relationship between the sides of a right triangle on a flat plane: square the lengths of the short sides, a and b, add those together, and you get the square of the length of the long side, c.
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This relationship, in some ways, actually distinguishes our normal, flat, Euclidean geometry from curved, non-Euclidean geometry. For example, a right triangle drawn on the surface of a sphere need not follow the Pythagorean theorem.
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2) Logarithms : Logarithms are the inverses, or opposites, of exponential functions. A logarithm for a particular base tells you what power you need to raise that base to to get a number. For example, the base 10 logarithm of 1 is log(1) = 0, since 1 = 10 0 ; log(10) = 1, since 10 = 10 1 ; and log(100) = 2, since 100 = 10 2 .
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The equation in the graphic, log(ab) = log(a) + log(b), shows one of the most useful applications of logarithms: they turn multiplication into addition.
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Until the development of the digital computer, this was the most common way to quickly multiply together large numbers, greatly speeding up calculations in physics, astronomy, and engineering.
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3) Calculus : The formula given here is the definition of the derivative in calculus. The derivative measures the rate at which a quantity is changing. For example, we can think of velocity, or speed, as being the derivative of position - if you are walking at 3 miles per hour, then every hour, you have changed your position by 3 miles.
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Naturally, much of science is interested in understanding how things change, and the derivative and the integral - the other foundation of calculus - sit at the heart of how mathematicians and scientists understand change.
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4) Law of Gravity : Newton's law of gravitation describes the force of gravity between two objects, F, in terms of a universal constant, G, the masses of the two objects, m 1 and m 2 , and the distance between the objects, r. Newton's law is a remarkable piece of scientific history - it explains, almost perfectly, why the planets move in the way they do. Also remarkable is its universal nature - this is not just how gravity works on Earth, or in our solar system, but anywhere in the universe.
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Newton's gravity held up very well for two hundred years, and it was not until Einstein's theory of general relativity that it would be replaced.
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5) The square root of -1 : Mathematicians have always been expanding the idea of what numbers actually are , going from natural numbers, to negative numbers, to fractions, to the real numbers. The square root of -1, usually written i , completes this process, giving rise to the complex numbers.
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Mathematically, the complex numbers are supremely elegant. Algebra works perfectly the way we want it to - any equation has a complex number solution, a situation that is not true for the real numbers : x 2 + 4 = 0 has no real number solution, but it does have a complex solution: the square root of -2. Calculus can be extended to the complex numbers, and by doing so, we find some amazing symmetries and properties of these numbers. Those properties make the complex numbers essential in electronics and signal processing.
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6) Euler's Polyhedra Formula : Polyhedra are the three-dimensional versions of polygons, like the cube to the right. The corners of a polyhedron are called its vertices, the lines connecting the vertices are its edges, and the polygons covering it are its faces.
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A cube has 8 vertices, 12 edges, and 6 faces. If I add the vertices and faces together, and subtract the edges, I get 8 + 6 - 12 = 2.
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Euler's formula states that, as long as your polyhedron is somewhat well behaved, if you add the vertices and faces together, and subtract the edges, you will always get 2. This will be true whether your polyhedron has 4, 8, 12, 20, or any number of faces.
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Euler's observation was one of the first examples of what is now called a topological invariant - some number or property shared by a class of shapes that are similar to each other. The entire class of "well-behaved" polyhedra will have V + F - E = 2. This observation, along with with Euler's solution to the Bridges of Konigsburg problem , paved the way to the development of topology, a branch of math essential to modern physics.
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7) Normal distribution : The normal probability distribution, which has the familiar bell curve graph to the left, is ubiquitous in statistics.
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The normal curve is used in physics, biology, and the social sciences to model various properties. One of the reasons the normal curve shows up so often is that it describes the behavior of large groups of independent processes .
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8) Wave Equation : This is a differential equation, or an equation that describes how a property is changing through time in terms of that property's derivative, as above. The wave equation describes the behavior of waves - a vibrating guitar string, ripples in a pond after a stone is thrown, or light coming out of an incandescent bulb. The wave equation was an early differential equation, and the techniques developed to solve the equation opened the door to understanding other differential equations as well.
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9) Fourier Transform : The Fourier transform is essential to understanding more complex wave structures, like human speech. Given a complicated, messy wave function like a recording of a person talking, the Fourier transform
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allows us to break the messy function into a combination of a number of simple waves, greatly simplifying analysis.
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The Fourier transform is at the heart of modern signal processing and analysis, and data compression.
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10) Navier-Stokes Equations : Like the wave equation, this is a differential equation. The Navier-Stokes equations describes the behavior of flowing fluids - water moving through a pipe, air flow over an airplane wing, or smoke rising from a cigarette. While we have approximate solutions of the Navier-Stokes equations that allow computers to simulate fluid motion fairly well, it is still an open question ( with a million dollar prize ) whether it is possible to construct mathematically exact solutions to the equations.
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11) Maxwell's Equations : This set of four differential equations describes the behavior of and relationship between electricity (E) and magnetism (H).
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Maxwell's equations are to classical electromagnetism as Newton's laws of motion and law of universal gravitation are to classical mechanics - they are the foundation of our explanation of how electromagnetism works on a day to day scale. As we will see, however, modern physics relies on a quantum mechanical explanation of electromagnetism, and it is now clear that these elegant equations are just an approximation that works well on human scales.
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12) Second Law of Thermodynamics : This states that, in a closed system, entropy (S) is always steady or increasing. Thermodynamic entropy is, roughly speaking, a measure of how disordered a system is. A system that starts out in an ordered, uneven state - say, a hot region next to a cold region - will always tend to even out, with heat flowing from the hot area to the cold area until evenly distributed.
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The second law of thermodynamics is one of the few cases in physics where time matters in this way. Most physical processes are reversible - we can run the equations backwards without messing things up. The second law, however, only runs in this direction. If we put an ice cube in a cup of hot coffee, we always see the ice cube melt, and never see the coffee freeze.
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13) Relativity : Einstein radically altered the course of physics with his theories of special and general relativity. The classic equation E = mc 2 states that matter and energy are equivalent to each other. Special relativity brought in ideas like the speed of light being a universal speed limit and the passage of time being different for people moving at different speeds.
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General relativity describes gravity as a curving and folding of space and time themselves, and was the first major change to our understanding of gravity since Newton's law. General relativity is essential to our understanding of the origins, structure, and ultimate fate of the universe.
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14) Schrodinger's Equation : This is the main equation in quantum mechanics. As general relativity explains our universe at its largest scales, this equation governs the behavior of atoms and subatomic particles.
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Modern quantum mechanics and general relativity are the two most successful scientific theories in history - all of the experimental observations we have made to date are entirely consistent with their predictions. Quantum mechanics is also necessary for most modern technology - nuclear power, semiconductor-based computers, and lasers are all built around quantum phenomena.
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15) Information Theory : The equation given here is for Shannon information entropy . As with the thermodynamic entropy given above, this is a measure of disorder. In this case, it measures the information content of a message - a book, a JPEG picture sent on the internet, or anything that can be represented symbolically. The Shannon entropy of a message represents a lower bound on how much that message can be compressed without losing some of its content.
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Shannon's entropy measure launched the mathematical study of information, and his results are central to how we communicate over networks today.
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16) Chaos Theory : This equation is May's logistic map . It describes a process evolving through time - x t+1 , the level of some quantity x in the next time period - is given by the formula on the right, and it depends on x t , the level of x right now. k is a chosen constant. For certain values of k, the map shows chaotic behavior: if we start at some particular initial value of x, the process will evolve one way, but if we start at another initial value, even one very very close to the first value, the process will evolve a completely different way.
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We see chaotic behavior - behavior sensitive to initial conditions - like this in many areas. Weather is a classic example - a small change in atmospheric conditions on one day can lead to completely different weather systems a few days later, most commonly captured in the idea of a butterfly flapping its wings on one continent causing a hurricane on another continent
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17) Black-Scholes Equation : Another differential equation, Black-Scholes describes how finance experts and traders find prices for derivatives. Derivatives - financial products based on some underlying asset, like a stock - are a major part of the modern financial system.
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The Black-Scholes equation allows financial professionals to calculate the value of these financial products, based on the properties of the derivative and the underlying asset.
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== Bibliothek :: Deutsches Zentrum für Altersfragen ==
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Die Bibliothek des Deutschen Zentrums für Altersfragen ==
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ist eine öffentlich zugängliche Präsenzbibliothek und Serviceeinrichtung. Sie verfügt über die umfangreichste Sammlung wissenschaftlicher und anwendungsorientierter Literatur zum Thema "Alter und Altern" im deutschsprachigen Raum.
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Sie suchen Literatur zum Thema Alter oder Altern? Recherchieren Sie in unserem Katalog:
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Bibliothekskatalog GeroLit
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https://www.dza.de/ueber-uns/bibliothek
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d22
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==..==
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==..==
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finePoem ==
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>> Großer und langsamer Wind
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>> Aus der Bibliothek des Meeres
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>> Hier darf ich ruhen
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>> [[Tomas Transtroemer]] (1931-2015)
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>> #poem #aki20 #dz20
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Hallo leute, das aktuelle gruppenfoto von MAI2020 sah ich vorhin auf der homepage vom cleveland museum of art. dort auch dieses mission statement vom feinsten:
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Creating transformative experiences
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for the benefit of
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all the people
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forever.
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=="(…) Das zweite Element, ==
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welches das studium aus dem Gleichgewicht bringt, möchte ich daher punctum nennen; den punctum, das meint auch: Stich, kleines Loch, kleiner Fleck, kleiner Schnitt – und Wurf der Würfel.
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Das punctum einer Photographie, das ist jenes Zufällige an ihr, das mich besticht (mich aber auch verwundet, trifft)."
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https://lustauflesen.de/die-helle-kammer ... #againwhatlearned ... 190220 via fb wg dem grossen zeh auf dem foto von marilyn monroe
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==Ein tool im Blended learning  ==
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==Ein tool im Personal training  ==
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incl. open archives
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https://groups.io/g/WISSEN2/topics
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Die wbg ist ein Verein zur Förderung von Wissenschaft und Bildung. Mit 85.000 Mitgliedern sind wir die größte Gemeinschaft für geisteswissenschaftliche Themen und bieten Gleichgesinnten ein Forum für Debatten. Jährlich veröffentlichen unsere Verlage mehr als 120 Publikationen aus den Bereichen Geschichte, Philosophie, Archäologie, Germanistik u.v.m. – oftmals Werke die ansonsten auf dem Buchmarkt nicht erscheinen könnten.
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Keine Liste mit Namen wissen2 vorhanden.
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Es gibt im Moment keine öffentlichen Mailinglisten Mailman auf dem Server listserv.shuttle.de.Um die Informationsseite einer nicht öffentlichen Liste zu besuchen, benutzen Sie eine URL wie jetzt, aber mit einem '/' und dem rechts Listennamen angehängt.
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Bei Fragen und Kommentaren senden Sie bitte an an mailman@listserv.shuttle.de.
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111119 via listserv.shuttle.de/mailman/listinfo/wissen2
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==Wenn man aber sagt==
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„Wenn man aber sagt:
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»Wie soll ich wissen, was er meint,
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ich sehe ja nur seine Zeichen«, so sage ich:
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»Wie soll er wissen, was er meint,
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er hat ja auch nur seine Zeichen.«“
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Ludwig Wittgenstein
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s.a.
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Stabsstelle
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„Wissen als Gemeingut“
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Niedersächsische Staats- und Universitätsbibliothek Göttingen | Bewerbungsfrist: 30.09.2019
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https://www.sub.uni-goettingen.de/wir-ueber-uns/stellenangebote-ausbildung/stellenangebot/mitarbeiter-in-wmd-e-13-tv-l-teilzeit-befristet/
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1708 via o.
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[[mailman]] liste incl. topics == test it ...
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== Modul [[JOBmooc]] für Jobsucher-innen ==
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http://wiki.aki-stuttgart.de/mediawiki/index.php/JOBmooc
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== Modul [[BIB]]mooc für BIB-leute ==
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http://wiki.aki-stuttgart.de/mediawiki/index.php/BIB
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... hashtag/wissen2 via fb ...
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https://www.facebook.com/hashtag/wissen2?source=feed_text&epa=HASHTAG
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E-learning und [[JOBmooc]] ==
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==2019==
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==2018==
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We hope that you will be able to attend
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and we look forward to your participation.
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Alle Vorteile des Skoobe Basic-Monatsabos:
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Unbegrenzt lesen
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Alle eBooks können Sie in voller Länge, beliebig lang und beliebig oft in der Skoobe-App lesen.
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Sie können Ihre Mitgliedschaft jederzeit ändern oder monatlich kündigen.
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091218 via thalia
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"When a truth is not given complete freedom,
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freedom is not complete." Vaclav Havel
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Stangl, W. (2018). Stichwort: 'Synästhesie'.
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Online Lexikon für Psychologie und Pädagogik.
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WWW: http://lexikon.stangl.eu/28/synaesthesie/ (2018-04-05)
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5300 Jahre Schrift===
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50 Beiträge zu 50 Schriftträgern
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http://dhd-blog.org/?p=8285
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210717 via fb
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GeoSpatial Semantics (GeoS) ==
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is an emerging research area of the spatial information sciences. This is why GeoS conference aims at providing a timely forum for prominent specialists, researchers, engineers and practitioners throughout the world to exchange the state-of-the-art research results in the areas of modeling and processing of GeoSpatial Semantics.  It has been largely recognized that GeoSpatial Semantics play a vital role for the development of the next-generation spatial databases and geographic information systems, as well as specialized geospatial web services.
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The original idea of GeoS conferences belongs to Dr. Sergei Levashkin (www.levashkin.com), the founder of conferences who year after year has been elected to perform the honorable positions of the President and Editor in Chief of the books of conference proceedings. To date, the four editions of the conference have attracted about 250 submissions, from which 69 regular and 8 short articles on the subject have been published in Volumes 3799, 4853, 5892, and 6631 of the Lecture Notes in Computer Science by Springer-Verlag.  Participants from 35 countries and 5 continents have attended GeoS conferences which were held at different locations in North America and Europe.  According to the Thomson-Reuters Institute of Scientific Information (ISI), the Springer-published books of proceedings arisen from GeoS are the most cited in the area of GeoSpatial Semantics in the world.
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http://www.geosco.org/
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110618 via site
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.
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Die Uni in Zeiten von Wiki, Blogs & Twitter
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von FobiKom-Weblog ...
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Prof. Christian Spannagel von der Pädagogischen Hochschule ist das Enfant terrible der Hochschuldidaktik und eLearning-Szene: Sehr kreativ, sehr anregend! Das Weblog der Staats- und Universitätsbibliothek Hamburg macht auf einen Bericht/ein Interview der Deutschen Welle mit Christian Spannagel aufmerksam. ...
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[[Holley Murchison]] ===
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-->
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Be a bit greener: please don't print this e-mail unnecessarily
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Be green: please don't print this e-mail until really needed
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300718 via f. + model20
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<!--
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==2017==
==2017==
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'''W2 bis 12.09.2017 incl. archive=='''
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  1. Turm zu Babel war 92 meter hoch (Karl Dietz)
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  2. Das globale Huhn u.a. (Karl Dietz)
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  3. KW37 ... [[OpenSpace]] 2017 (Karl Dietz)
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  1209
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  1. Maschinelle Erschliessung in der [[DNB]] (Karl Dietz)
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  2. Stellen ... BIBchatDE ... VAB (Karl Dietz)
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  3. Objects stolen from the University of Bergen Museum (Karl Dietz)
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  4. Lesung der Menschenrechtscharta - 06.09. (Karl Dietz)
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  5. [[Jack Kerouac]] (1922-1969) (Karl Dietz)
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  0509
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  1. Pilzmuseum in Cernier (Karl Dietz)
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  2. Dossier Integration ... Studie (Karl Dietz)
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  3. KW30 ... VAB 2017 (Karl Dietz)
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  4. Re: KW30 ... VAB 2017 (Ingrid.Strauch)
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  5. ARCHIVAR Schwerpunkt "freie Archive" (Karl Dietz)
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  6. Maschinelle Erschliessung in der [[DNB]] (Karl Dietz)
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  0108
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  1. Robert Kurz (1943-2012) (Karl Dietz)
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  2. Modulare wiss. Weiterbildung ... (Karl Dietz)
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  3. Gr?ne Schr.-Reihe incl. Kurt Kretschmann (Karl Dietz)
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  4. [[Walter Benjamin]] (1892-1940) (Karl Dietz)
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  5. Tobias Meissner (1966-2016) en vikipedio (Karl Dietz)
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  1807
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  1. Re: Theodor Bergmann (1916-2017) (Ingrid.Strauch)
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  2. Recherche ... OpenSpace 2017 (Karl Dietz)
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  3. 10 Jahre [[Europeana]] in 2018 (Karl Dietz)
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  4. Theodor Bergmann (1916-2017) (Karl Dietz)
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  0407
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  1. The trouble with "modernity" via public books (Karl Dietz)
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  2. Theodor Bergmann (1916-2017) (Karl Dietz) ... via ND
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  3. Re: [[Theo Bergmann]] (1916-2017) (Karl Dietz) ... via stz
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  1306
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   1. Fragebogen von Max Frisch (Karl Dietz)
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   1. Fragebogen von [[Max Frisch]] (Karl Dietz)
   2. SommerOpenSpace 2017 ... SOS2017 (Karl Dietz)
   2. SommerOpenSpace 2017 ... SOS2017 (Karl Dietz)
   3. Re: Steven Pelcman ... (Karl Dietz)
   3. Re: Steven Pelcman ... (Karl Dietz)
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   2. [[Ivan Illich]] (1926-2002) (Karl Dietz)
   2. [[Ivan Illich]] (1926-2002) (Karl Dietz)
   3. Re: B?cherverbrennung - 10.05.1933 (Karl Dietz)
   3. Re: B?cherverbrennung - 10.05.1933 (Karl Dietz)
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   4. Re: Paulo Freire (1921-1977) (Karl Dietz)
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   4. Re: [[Paulo Freire]] (1921-1977) (Karl Dietz)
   5. Yasar Kemal (1923-2015) (Karl Dietz)
   5. Yasar Kemal (1923-2015) (Karl Dietz)
   1305
   1305
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   1. Re: KW13 ... [[OpenSpace]] [[2017]] ([[Karl Dietz]])
   1. Re: KW13 ... [[OpenSpace]] [[2017]] ([[Karl Dietz]])
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  2. Re: KW13 ... OpenSpace 2017 (Karl Dietz)
 
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  3. Re: KW13 ... OpenSpace 2017 (Karl Dietz)
 
   3103
   3103
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   1. RADAR ? ein neues Angebot f?r die Archivierung und
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   1. RADAR ? ein neues Angebot f?r die Archivierung und Publikation von Forschungsdaten
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      Publikation von Forschungsdaten (Karl Dietz)
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   2. Victor Hugo: How to be a Grandfather (Karl Dietz)
   2. Victor Hugo: How to be a Grandfather (Karl Dietz)
   3. BLOG2014 ... (Karl Dietz)
   3. BLOG2014 ... (Karl Dietz)
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   1. IFB ... DNB ... (Karl Dietz)
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   1. [[IFB]] ... [[DNB]] ...  
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   2. == Bibliothek der Freien == (Karl Dietz)
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   2. == [[Bibliothek der Freien]] == (Karl Dietz)
   3. Re: Jenseits der Schriftkultur (Karl Dietz)
   3. Re: Jenseits der Schriftkultur (Karl Dietz)
   4. [[PMEST]]-searching (Karl Dietz)
   4. [[PMEST]]-searching (Karl Dietz)
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   1. Re: Right to copy (Karl Dietz)
   1. Re: Right to copy (Karl Dietz)
   2. Re: == [[Bibliothek der Freien]] == (Karl Dietz)
   2. Re: == [[Bibliothek der Freien]] == (Karl Dietz)
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   3. S?lo Soy Un Guitarrista - [[Bob Dylan]] (Karl Dietz)
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   3. Solo Soy Un Guitarrista - [[Bob Dylan]] (Karl Dietz)
   4. Re: [[Google]] ... (Karl Dietz)
   4. Re: [[Google]] ... (Karl Dietz)
   5. [[Pablo Picasso]] (1881-1973) (Karl Dietz)
   5. [[Pablo Picasso]] (1881-1973) (Karl Dietz)
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   1. [[Annemarie Schwarzenbach]] (1908 - 1942) (Karl Dietz)
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   1. [[Annemarie Schwarzenbach]] (1908-1942) (Karl Dietz)
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   2. Re: [InetBib] adlr.link gestartet - Fachinformationsdienst
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   2. Re: [InetBib] adlr.link gestartet ...
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      f?r Medien- und Kommunikationswissenschaften (Karl Dietz)
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   3. 40 Jahre Lektoratskooperation (Karl Dietz)
   3. 40 Jahre Lektoratskooperation (Karl Dietz)
   4. Re: Reiss-Engelhorn-Museen versus [[Wikipedia]] (Karl Dietz)
   4. Re: Reiss-Engelhorn-Museen versus [[Wikipedia]] (Karl Dietz)
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   5. Re: Sci hub ... [[Bibliotheken]] ... (Karl Dietz)
   5. Re: Sci hub ... [[Bibliotheken]] ... (Karl Dietz)
   3004
   3004
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   1. Re: Dietrich Bonhoeffer (1906-1945) ... IS ... [[VAB]]
   1. Re: Dietrich Bonhoeffer (1906-1945) ... IS ... [[VAB]]
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   2. Robert Dilts: Dynamic Learning (Karl Dietz)
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   2. [[Robert Dilts]]: Dynamic Learning (Karl Dietz)
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   4. [[Paul G. Christaller]] (1860-1950) (Karl Dietz)
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   4. Paul G. Christaller (1860-1950) (Karl Dietz) ...  s.a. [[Paul Christaller]]
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   2. Kalliope zu [[Marianne Buder]] (Karl Dietz)
   3. Dead Tree Lovers coming to #32c3: Call for Books (Karl Dietz)
   3. Dead Tree Lovers coming to #32c3: Call for Books (Karl Dietz)
   4. Eduard Winkler (1799-1862) (Karl Dietz)
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   2. [[Bibliotheken]] in Stuttgart (Karl Dietz)
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   3. Unterricht - Digitale Schulb?cher in der Erprobungsphase     (Karl Dietz)
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   3. Unterricht - Digitale Schulb?cher in der Erprobungsphase     elife
   4. Datenbanken. Anatomia Collection. UIMA. (Karl Dietz)
   4. Datenbanken. Anatomia Collection. UIMA. (Karl Dietz)
   5. Erich Ribolits in Streifzuege 56/2012 (Karl Dietz)
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>> Aus der Bibliothek des Meeres
 
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==2014==
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   3. Schmetterling und Taucherglocke (Karl Dietz)
   3. Schmetterling und Taucherglocke (Karl Dietz)
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   5. [[Hans A. Pestalozzi]] + 14. Juli 2004
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   6. Zedler - die gr?sste Enzyklop?die des 18. Jh. (Karl Dietz)
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   5. Mr. Wu + kallias + dib re:launch (Karl Dietz)
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   1. [[Datenbanken]] via Reference Global (Karl Dietz)
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   4. Rachel Carson Center, Muenchen (Karl Dietz)
   4. Rachel Carson Center, Muenchen (Karl Dietz)
   5. John Zorn: KristallNacht ... (Karl Dietz)
   5. John Zorn: KristallNacht ... (Karl Dietz)
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* wer aus [[AKI]]20 ==
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   1. [[Emmi Pikler]]. listen. [[Picasa]]  
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oder openspace oder moox oder ... in die w2 mag? einfach sagen. k.
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   3. ... noch ein Gedicht? advent10 ... (Karl Dietz)
   4.  ...Urheberrecht auf 4'33'' Stille ... (Karl Dietz)
   4.  ...Urheberrecht auf 4'33'' Stille ... (Karl Dietz)
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040623
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Aktuelle Version vom 4. Juni 2023, 18:39 Uhr


Inhaltsverzeichnis

W2 // WISSEN2

W2 per Facebook group== https://www.facebook.com/groups/wissen2/

WISSEN2 per AKI-wiki== http://wiki.aki-stuttgart.de

...

WISSEN2 ist ein modul im Blended learning & Personal training==

...

  • Kontakt: Karl Dietz
  • karl.dz@gmail.com
  • Tel. 0172 / 768 7976


The 17 Equations That Changed The World

1) The Pythagorean Theorem : This theorem is foundational to our understanding of geometry. It describes the relationship between the sides of a right triangle on a flat plane: square the lengths of the short sides, a and b, add those together, and you get the square of the length of the long side, c.

This relationship, in some ways, actually distinguishes our normal, flat, Euclidean geometry from curved, non-Euclidean geometry. For example, a right triangle drawn on the surface of a sphere need not follow the Pythagorean theorem.

2) Logarithms : Logarithms are the inverses, or opposites, of exponential functions. A logarithm for a particular base tells you what power you need to raise that base to to get a number. For example, the base 10 logarithm of 1 is log(1) = 0, since 1 = 10 0 ; log(10) = 1, since 10 = 10 1 ; and log(100) = 2, since 100 = 10 2 .

The equation in the graphic, log(ab) = log(a) + log(b), shows one of the most useful applications of logarithms: they turn multiplication into addition.

Until the development of the digital computer, this was the most common way to quickly multiply together large numbers, greatly speeding up calculations in physics, astronomy, and engineering.

3) Calculus : The formula given here is the definition of the derivative in calculus. The derivative measures the rate at which a quantity is changing. For example, we can think of velocity, or speed, as being the derivative of position - if you are walking at 3 miles per hour, then every hour, you have changed your position by 3 miles.

Naturally, much of science is interested in understanding how things change, and the derivative and the integral - the other foundation of calculus - sit at the heart of how mathematicians and scientists understand change.

4) Law of Gravity : Newton's law of gravitation describes the force of gravity between two objects, F, in terms of a universal constant, G, the masses of the two objects, m 1 and m 2 , and the distance between the objects, r. Newton's law is a remarkable piece of scientific history - it explains, almost perfectly, why the planets move in the way they do. Also remarkable is its universal nature - this is not just how gravity works on Earth, or in our solar system, but anywhere in the universe.

Newton's gravity held up very well for two hundred years, and it was not until Einstein's theory of general relativity that it would be replaced.

5) The square root of -1 : Mathematicians have always been expanding the idea of what numbers actually are , going from natural numbers, to negative numbers, to fractions, to the real numbers. The square root of -1, usually written i , completes this process, giving rise to the complex numbers.

Mathematically, the complex numbers are supremely elegant. Algebra works perfectly the way we want it to - any equation has a complex number solution, a situation that is not true for the real numbers : x 2 + 4 = 0 has no real number solution, but it does have a complex solution: the square root of -2. Calculus can be extended to the complex numbers, and by doing so, we find some amazing symmetries and properties of these numbers. Those properties make the complex numbers essential in electronics and signal processing.

6) Euler's Polyhedra Formula : Polyhedra are the three-dimensional versions of polygons, like the cube to the right. The corners of a polyhedron are called its vertices, the lines connecting the vertices are its edges, and the polygons covering it are its faces.

A cube has 8 vertices, 12 edges, and 6 faces. If I add the vertices and faces together, and subtract the edges, I get 8 + 6 - 12 = 2.

Euler's formula states that, as long as your polyhedron is somewhat well behaved, if you add the vertices and faces together, and subtract the edges, you will always get 2. This will be true whether your polyhedron has 4, 8, 12, 20, or any number of faces.

Euler's observation was one of the first examples of what is now called a topological invariant - some number or property shared by a class of shapes that are similar to each other. The entire class of "well-behaved" polyhedra will have V + F - E = 2. This observation, along with with Euler's solution to the Bridges of Konigsburg problem , paved the way to the development of topology, a branch of math essential to modern physics.

7) Normal distribution : The normal probability distribution, which has the familiar bell curve graph to the left, is ubiquitous in statistics.

The normal curve is used in physics, biology, and the social sciences to model various properties. One of the reasons the normal curve shows up so often is that it describes the behavior of large groups of independent processes .

8) Wave Equation : This is a differential equation, or an equation that describes how a property is changing through time in terms of that property's derivative, as above. The wave equation describes the behavior of waves - a vibrating guitar string, ripples in a pond after a stone is thrown, or light coming out of an incandescent bulb. The wave equation was an early differential equation, and the techniques developed to solve the equation opened the door to understanding other differential equations as well.

9) Fourier Transform : The Fourier transform is essential to understanding more complex wave structures, like human speech. Given a complicated, messy wave function like a recording of a person talking, the Fourier transform allows us to break the messy function into a combination of a number of simple waves, greatly simplifying analysis. The Fourier transform is at the heart of modern signal processing and analysis, and data compression.

10) Navier-Stokes Equations : Like the wave equation, this is a differential equation. The Navier-Stokes equations describes the behavior of flowing fluids - water moving through a pipe, air flow over an airplane wing, or smoke rising from a cigarette. While we have approximate solutions of the Navier-Stokes equations that allow computers to simulate fluid motion fairly well, it is still an open question ( with a million dollar prize ) whether it is possible to construct mathematically exact solutions to the equations.

11) Maxwell's Equations : This set of four differential equations describes the behavior of and relationship between electricity (E) and magnetism (H).

Maxwell's equations are to classical electromagnetism as Newton's laws of motion and law of universal gravitation are to classical mechanics - they are the foundation of our explanation of how electromagnetism works on a day to day scale. As we will see, however, modern physics relies on a quantum mechanical explanation of electromagnetism, and it is now clear that these elegant equations are just an approximation that works well on human scales.

12) Second Law of Thermodynamics : This states that, in a closed system, entropy (S) is always steady or increasing. Thermodynamic entropy is, roughly speaking, a measure of how disordered a system is. A system that starts out in an ordered, uneven state - say, a hot region next to a cold region - will always tend to even out, with heat flowing from the hot area to the cold area until evenly distributed.

The second law of thermodynamics is one of the few cases in physics where time matters in this way. Most physical processes are reversible - we can run the equations backwards without messing things up. The second law, however, only runs in this direction. If we put an ice cube in a cup of hot coffee, we always see the ice cube melt, and never see the coffee freeze.

13) Relativity : Einstein radically altered the course of physics with his theories of special and general relativity. The classic equation E = mc 2 states that matter and energy are equivalent to each other. Special relativity brought in ideas like the speed of light being a universal speed limit and the passage of time being different for people moving at different speeds.

General relativity describes gravity as a curving and folding of space and time themselves, and was the first major change to our understanding of gravity since Newton's law. General relativity is essential to our understanding of the origins, structure, and ultimate fate of the universe.

14) Schrodinger's Equation : This is the main equation in quantum mechanics. As general relativity explains our universe at its largest scales, this equation governs the behavior of atoms and subatomic particles.

Modern quantum mechanics and general relativity are the two most successful scientific theories in history - all of the experimental observations we have made to date are entirely consistent with their predictions. Quantum mechanics is also necessary for most modern technology - nuclear power, semiconductor-based computers, and lasers are all built around quantum phenomena.

15) Information Theory : The equation given here is for Shannon information entropy . As with the thermodynamic entropy given above, this is a measure of disorder. In this case, it measures the information content of a message - a book, a JPEG picture sent on the internet, or anything that can be represented symbolically. The Shannon entropy of a message represents a lower bound on how much that message can be compressed without losing some of its content.

Shannon's entropy measure launched the mathematical study of information, and his results are central to how we communicate over networks today.

16) Chaos Theory : This equation is May's logistic map . It describes a process evolving through time - x t+1 , the level of some quantity x in the next time period - is given by the formula on the right, and it depends on x t , the level of x right now. k is a chosen constant. For certain values of k, the map shows chaotic behavior: if we start at some particular initial value of x, the process will evolve one way, but if we start at another initial value, even one very very close to the first value, the process will evolve a completely different way.

We see chaotic behavior - behavior sensitive to initial conditions - like this in many areas. Weather is a classic example - a small change in atmospheric conditions on one day can lead to completely different weather systems a few days later, most commonly captured in the idea of a butterfly flapping its wings on one continent causing a hurricane on another continent . 17) Black-Scholes Equation : Another differential equation, Black-Scholes describes how finance experts and traders find prices for derivatives. Derivatives - financial products based on some underlying asset, like a stock - are a major part of the modern financial system.

The Black-Scholes equation allows financial professionals to calculate the value of these financial products, based on the properties of the derivative and the underlying asset.


Bibliothek :: Deutsches Zentrum für Altersfragen

Die Bibliothek des Deutschen Zentrums für Altersfragen == ist eine öffentlich zugängliche Präsenzbibliothek und Serviceeinrichtung. Sie verfügt über die umfangreichste Sammlung wissenschaftlicher und anwendungsorientierter Literatur zum Thema "Alter und Altern" im deutschsprachigen Raum.

Sie suchen Literatur zum Thema Alter oder Altern? Recherchieren Sie in unserem Katalog: Bibliothekskatalog GeroLit

https://www.dza.de/ueber-uns/bibliothek

d22

..

..

finePoem == 

>> Großer und langsamer Wind
>> Aus der Bibliothek des Meeres
>> Hier darf ich ruhen
>> Tomas Transtroemer (1931-2015)
>> #poem #aki20 #dz20


Hallo leute, das aktuelle gruppenfoto von MAI2020 sah ich vorhin auf der homepage vom cleveland museum of art. dort auch dieses mission statement vom feinsten:

Creating transformative experiences for the benefit of all the people forever.

"(…) Das zweite Element,

welches das studium aus dem Gleichgewicht bringt, möchte ich daher punctum nennen; den punctum, das meint auch: Stich, kleines Loch, kleiner Fleck, kleiner Schnitt – und Wurf der Würfel. Das punctum einer Photographie, das ist jenes Zufällige an ihr, das mich besticht (mich aber auch verwundet, trifft)." https://lustauflesen.de/die-helle-kammer ... #againwhatlearned ... 190220 via fb wg dem grossen zeh auf dem foto von marilyn monroe




Be a bit greener: please don't print this e-mail unnecessarily

Be green: please don't print this e-mail until really needed

300718 via f. + model20



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