What, When, Where, How, Who?
Absoluteness
Introduction, Important Definitions and Related Concepts:
In mathematical logic, a formula is said to be absolute if it has the same truth value in each of some class of structures. Theorems about absoluteness typically show that each of a large syntactic class of formulas is absolute. Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".[2] Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. In mathematics and in the sciences, a formula (plural: formulae, formulæ or formulas) is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. One of many famous formulae is Albert Einstein's E = mc² (see special relativity). Structure is a fundamental and sometimes intangible notion covering the recognition, observation, nature, and stability of patterns and relationships of entities. From a child's verbal description of a snowflake, to the detailed scientific analysis of the properties of magnetic fields, the concept of structure is an essential foundation of nearly every mode of inquiry and discovery in science, philosophy, and art.[1] Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Science considers space to be a fundamental quantity (a quantity which can not be defined via other quantities because other quantities — like force and energy — are already defined via space). Thus an operational definition is used in which the procedure of measurement of space intervals (distances) and the units of measurement are defined. Change denotes the transition that occurs between one state to another. Ovid produced a classic thematic handling of change as metamorphosis in his Metamorphoses. Benjamin Peirce (pronounced /ˈpɜrs/ purse[1]), April 4, 1809 – October 6, 1880) was an American mathematician who taught at Harvard University for forty years. He made contributions to celestial mechanics, number theory, algebra, and the philosophy of mathematics.
Classical antiquity and the study of "the classics", refers to the culture of Ancient Greece or Rome."High classical" refers to Greek art associated mainly with Athens and the works atop the Acropolis. The Greeks (Greek: Έλληνες, IPA: [ˈelines]) are a nation and ethnic group who have populated Greece and the area of the Aegean Sea for over 3,500 years.[14] Today they are primarily found in the Balkan peninsula of southeastern Europe, the Greek islands, Cyprus, and throughout the world as part of the Greek diaspora. Logos (Greek λόγος) is an important term in philosophy, analytical psychology, rhetoric and religion. It derives from the verb λέγω legō: to count, tell, say, or speak.[1] Inference is the act or process of deriving a conclusion based solely on what one already knows. Inference is studied within several different fields. In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true, within the accepted standards of the field. A proof is a logical argument, not an empirical one. In mathematical logic, a formal calculation is sometimes defined as a calculation which is systematic, but without a rigorous justification. This means that we are manipulating the symbols in an expression using a generic substitution, without proving that the necessary conditions hold. Science (from the Latin scientia, 'knowledge'), in the broadest sense, refers to any systematic knowledge or practice. In a more restricted sense, science refers to a system of acquiring knowledge based on the scientific method, as well as to the organized body of knowledge gained through such research.[1][2] System (from Latin systēma, in turn from Greek σύστημα systēma) is a set of interacting or interdependent entities, real or abstract, forming an integrated whole. The concept of an 'integrated whole' can also be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other elements, and from relationships between an element of the set and elements not a part of the relational regime. A chemical formula is a concise way of expressing information about the atoms that constitute a particular chemical compound. A chemical formula is also a short way of showing how a chemical reaction occurs. Albert Einstein (German: IPA: [ˈalbɐt ˈaɪ̯nʃtaɪ̯n] (Audio file) ; English: IPA: /ˈælbɝt ˈaɪnstaɪn/) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist. He is best known for his theory of relativity and specifically mass-energy equivalence, E = mc2. Example:
Shape Transition and Propulsive Force of an Elastic Rod Rotating in a Viscous Fluid Bian Qian, Thomas R. Powers, and Kenneth S. Breuer
(Received 2 December 2007; published 19 February 2008) The deformation of an elastic rod rotating in a viscous fluid is considered, with applications related to flagellar motility. The rod is tilted relative to the rotation axis, and experiments and theory are used to study the shape transition when driven either at constant torque or at constant speed. At low applied torque, the rod bends gently and generates small propulsive force. At a critical torque, the rotation speed increases abruptly, and the rod forms a helical shape with increased propulsive force. We find good agreement between theory and experiment. A simple physical model is presented to capture and explain the essential behavior. (Ref. Physical Review Letters). Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic kinematics (see mass in special relativity and mass in General Relativity). Another Example:
Flow, Ordering, and Jamming of Sheared Granular Suspensions Denis S. Grebenkov,2,3 Massimo Pica Ciamarra,1,2 Mario Nicodemi,2,4 and Antonio Coniglio2
(Received 16 July
2007; published 19 February 2008) We
study the rheological properties
of a granular suspension subject to
constant shear stress by constant
volume molecular dynamics simulations.
We derive the system “flow
diagram” in the volume fraction or
stress plane (
,
F): at low
the flow is disordered, with
the viscosity obeying a Bagnold-like
scaling only at small F
and diverging as the jamming point is
approached; if the shear
stress is strong enough, at higher
an ordered flow regime is found,
the order-disorder transition being
marked by a sharp drop of the
viscosity. A broad jamming
region is also observed where, in
analogy with the glassy
region of thermal systems, slow dynamics
followed by kinetic arrest
occurs when the ordering transition is
prevented. (Ref.
Physical Review Letters). Special
relativity (SR) (aka the special
theory of relativity (STR)) is the
physical theory of
measurement in
inertial frames of reference
proposed in
1905 by
Albert Einstein in the paper "On
the Electrodynamics of Moving Bodies".[1]
It generalizes
Galileo's principle of relativity —
that all
uniform motion is relative, and that
there is no absolute and well-defined
state of rest (no
privileged reference frames) — from
mechanics to all the
laws of physics, including both the
laws of mechanics and of
electrodynamics, whatever they may
be. Snowflake is A particle of
snow, an aggregate of ice crystals
that forms while falling in and below a
cloud. A magnetized bar
has its power concentrated at two ends,
its poles; they are known as its
north (N) and south (S) poles, because
if the bar is hung by its middle from a
string, its N end tends to point
northwards and its S end southwards. The
N end will repel the N end of another
magnet, S will repel S, but N and S
attract each other. Philosophy
is the discipline concerned with
questions of how one should live (ethics);
what sorts of things exist and what are
their essential natures (metaphysics);
what counts as genuine knowledge (epistemology);
and what are the correct principles of
reasoning (logic).[1][2]
The word is of
Greek
origin: φιλοσοφία (philosophía),
meaning love of wisdom.[3]
Art refers to a diverse
range of human activities and artifacts,
and may be used to cover all or any of
the arts, including
music,
literature and other forms. It is
most often used to refer specifically to
the
visual arts, including media such as
painting,
sculpture, and
printmaking. Quality in
everyday life and business, engineering
and manufacturing has a
pragmatic interpretation as the
non-inferiority, superiority
or
usefulness of something. This is
the most common interpretation of the
term. The word originates from
Latin substantia, literally
meaning "standing under". The word was
used to translate the
Greek philosophical term
ousia.
- Relation (mathematics), a generalization of arithmetic relations, such as "=" and "<", that occur in statements, such as "5 < 6" and "2 + 2 = 4". See also binary relation, triadic relation, relational algebra, theory of relations. In the relational model of databases, a set of tuples (also called rows), otherwise known as a table. Fundamental means serving as an original or generating source : primary <a discovery fundamental to modern computers> b: serving as a basis supporting existence or determining essential structure or function : basic2 a: of or relating to essential structure, function, or facts : radical <fundamental change>; also : of or dealing with general. In physics, force is what causes a mass to accelerate. It may be experienced as a twist, a push, or a pull. In physics and other sciences, energy (from the Greek ενεργός, energos, "active, working")[1] is a scalar physical quantity that is a property of objects and systems which is conserved by nature. Energy is often defined as the ability to do work. An operational definition is a showing of something — such as a variable, term, or object — in terms of the specific process or set of validation tests used to determine its presence and quantity. Properties described in this manner must be publicly accessible so that persons other than the definer can independently measure or test for them at will. In science, however, where accurate measurement is crucial, a measurement is understood to have three parts: first, the measurement itself, second, the margin of error, and third, the confidence level -- that is, the probability that the actual property of the physical object is within the margin of error. For example, we might measure the length of an object as 2.34 meters plus or minus 0.01 meter, with a 95% level of confidence. Distance is a numerical description of how far apart objects are at any given moment in time. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria (e.g. "two counties over"). In topology, a transition function is a homeomorphism from one coordinate chart to another. Given two charts (Ui, φi) and (Uj, φj) a transition function normally takes the form
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6 (six) is the natural number following 5 and preceding 7. The SI prefix for 10006 is exa (E), and for its reciprocal atto (a). Year 1880 (MDCCCLXXX) was a leap year starting on Thursday (link will display the full calendar) of the Gregorian calendar (or a leap year starting on Tuesday of the 12-day slower Julian calendar).