Bruno (Nature-picture):

(1548-1600) Italian Dominican friar, philosopher, mathematician, known for his cosmological theories, which extended the Copernican model; he proposed that the universe is infinite & could have no "center”, the stars were distant suns surrounded by their own planets & raised the possibility that these planets might foster life of their own (cosmic pluralism).  He was burned at the stake in Rome in 1600.  He was a man of the early Summer, an age of ripening consciousness & earliest urban & critical stirrings; we find in him the beginning of a purely philosophical form of the world-feeling, and opposition between idealistic and realistic systems.

 

Newton (Nature-picture):

(1642–1727) likewise a man of the Summer, who helped give birth to the formation of a new mathematic conception, of number as copy & content of world-form.

 

Goethe (Nature-picture):

(1749-1832) a man of the Autumn, a period when the intelligence of the city achieves the zenith of strict intellectual creativeness, an age when the great conclusive systems (Kant, Hegel) were built.

 

work (physics):

the energy transferred to or from an object via the application of force along a displacement, often represented as the product of force and displacement; a scalar quantity, with only magnitude & no direction.  It transfers energy from one place to another or one form to another. The externally measured forces & external effects may be electromagnetic, gravitational, or pressure/volume or other macroscopically mechanical variables.

 

First Law of Thermodynamics:

law of conservation of energy adapted for thermodynamic processes, distinguishing 2 kinds of transfer of energy, as heat & as thermodynamic work, relating them to a function of a body's state, called internal energy.  The conservation of energy states that the total energy of an isolated system is constant, can be transformed from one form to another, but can be neither created nor destroyed.

 

JR Mayer:

see above page 378, 393 & 412

 

Socialist theory (birth):

In the late 18th century, the steam engine powered the Industrial Revolution bringing sweeping economic & social change first to UK & then the rest of Europe & capitalism thrived.  Socialism was a response to the expanding capitalist system, an alternative, aimed at helping the working class & creating a more egalitarian society.  Three leading socialist pioneers were: Henri de Saint-Simon (1760–1825), Robert Owen (1771–1858) & Charles Fourier (1772–1837),  all offering their own models for social organization based on cooperation not competition.  Marx (1818-1883) was the most influential theorist of socialism; his 1848 work The Communist Manifesto argued that true “scientific socialism” could be established only after a revolutionary class struggle, with the workers emerging on top.

 

work (economic):

aka wage labour; socioeconomic relationship between worker & employer in which the worker sells their labour under a formal or informal employment contract, in a market-determined (supply demand principles) labour market, in exchange for money paid as wages (short-term work) or salaries (permanent employment); the work product becomes the undifferentiated property of the employer.

 

Adam Smith:

(1723-1790) Scottish economist & philosopher, known as ''The Father of Economics'' for his classic work the Wealth of Nations (1776), a precursor to the discipline of economics & foundation of classical free market economic theory; he developed the concept of division of labour & expounded upon how rational self-interest and competition can lead to economic prosperity.

 

vis a vis:

French, compared with, in relation to or toward

 

Quesney:

(1694-1774) French economist & physician, leading thinker of the physiocratic school, famous for his “Tableau économique" (Economic Table) of 1758, which provided the foundations of the ideas for the Physiocrats, a first attempt at describing the economy in an analytical way.  He argued that trade & industry were not sources of wealth, and instead agricultural surpluses flowing through the economy (as rent, wages & purchases) were the real economic movers.  

 

Turgot:

(1727-1781) aka Anne Robert Jacques Turgot, Baron de l'Aulne, French economist & statesman, a leading a physiocrat, who evolved into an economic liberal; first economist to have recognized the law of diminishing marginal returns in agriculture

 

conservation of energy:

the total energy of an isolated system remains constant, conserved over time; first proposed & tested by Émilie du Châtelet, it means energy can neither be created nor destroyed but only transformed or transferred from one form to another.

 

entropy:

in physics, a function of thermodynamic variables (as temperature, pressure, or composition) showing the quantity of energy not available for work during a thermodynamic process; a closed system evolves toward a state of maximum entropy.

 

least action:

see above page 412

 

17th Century (force): * see EndNote<A>

The work 'On the Revolutions of the Heavenly Spheres (1543, Copernicus) began the Scientific Revolution.  A new method based on empirical, systematic experimentation & inductive methodology (Bacon 1561-1626; W Gilbert 1544-1603) replaced Aristotelian deduction & Scholastic philosophy.  Copernicus (1473-1543), Galileo (1564-1642) & Kepler (1571-1630) challenged the Ptolemaic universe.  A new paradigm built on developments in mathematics, physics, astronomy & biology began.  Thinkers like Descartes (1596-1650) looked to a mechanical, mathematical world, to be known through experimental research.  Newton dealt Aristotelian physics a mortal blow with his grand synthesis (Principia, 1687) formulating the laws of motion & universal gravitation, the new cosmology.  

 

18th Century (force): * see Endnote<B>

Classical mechanics, based on Newton & Leibniz advanced in the 18th century, especially in the area of celestial mechanics.  Laplace (1749-1827) used Newton’s tool; his Celestial Mechanics (1799–1825) replaced geometry with calculus & applied it to astronomical objects.  He was a pioneer of mathematical physics, with the Laplace's equation & Laplace transform.  Another Frenchman, Lagrange (1736-1813) reformulated the principles of classical mechanics where he emphasized energy more than force.  He attempted the 3-body problem, analysed the stability of planetary orbits & discovered the existence of the Lagrangian points.  He developed a method to use a single polar coordinate equation to describe any orbit, including parabolic & hyperbolic types, useful for calculating the behaviour of planets, comets & spacecraft trajectories.  With mechanistic determinism, the role of mathematics in science became increasingly prominent.

 

Culture at its end (pure analysis): * see EndNote<C>

branch of mathematics dealing with limits & related theories (differentiation, integration, measure, infinite series, analytic functions), studied in the context of real & complex numbers and functions.  Unlike geometry it can be applied to any space of mathematical objects such as topologic space or metric space

 

theory of functions of several complex variables: * see EndNote<D>

branch of mathematics dealing with complex-valued functions on the complex coordinate space Cn of n-tuples of complex numbers; it is a sub branch of complex analysis that investigates functions of complex numbers.  Employed in algebraic geometry, number theory, analytic combinatorics, applied mathematics as well as in physics (hydrodynamics, thermodynamics, quantum mechanics).  The use of complex analysis has applications in engineering (nuclear, aerospace, mechanical & electrical engineering).

 

Physics (end of the 19th Century):

By the late 19th century classical mechanics could cope with highly complex problems involving macroscopic situations; thermodynamics & kinetic theory were established; geometrical and physical optics were understood in terms of electromagnetic waves; the conservation laws for energy, momentum & mass were accepted.  It was beleived all important laws of physics had been discovered & any future research would involve clearing up minor problems.  However in 1900 doubts emerged about the completeness of the classical theories.  Maxwell's theories ( )  were undermined by inadequacies & their inability to explain certain physical phenomena (notably energy distribution in blackbody radiation, and photoelectric effect).  also owwringly, other theoretical formulations led to paradoxes when pushed to the limit.  These shortcomings were never resolved.  New ideas were required.  At the beginning of the 20th century a major revolution shook the world of physics, the era of modern physics