Riemann for Anti-Dummies

"Now, given that the future of civilization depends on diminishing the attractiveness of being a dummy, we will introduce, from time to time over the coming period, a series of pedagogical discussions, on the above-titled subject, "Riemann for Anti-Dummies." This investigation will take us through the development of what has been generally called Gauss' and Riemann's theory of functions. While formal mathematical presentations of this subject abound, both in a form suited for high priests of mathematical and computer sciences, and also in a form more suited "for dummies," virtually all these surveys lack any real understanding of the thinking underlying Gauss' and Riemann's discoveries. From our standpoint it were more appropriate to characterize the Gauss/Riemann theory of functions, as a metaphorical science, rather than a formal mathematical one. That being the case, we will avoid beginning with a formal definition of a function, preferring to leave such matters unstated, so that the reader can construct a concept, rather than learn a definition."

A Pedagogical series by Bruce Director

# Article Title
1 Riemann for Anti-Dummies: Part 1
2 Riemann for Anti-Dummies: Part 2
3 Riemann for Anti-Dummies: Part 3 : On Kepler
4 Riemann for Anti-Dummies: Part 4
5 Riemann for Anti-Dummies: Part 5
6 Riemann for Anti-Dummies: Part 6
7 Riemann for Anti-Dummies: Part 7 : Towards a Hylozoic Calculus
8 Riemann for Anti-Dummies: Part 8 : The Significance of Precise Ambiguity in Science
9 Riemann for Anti-Dummies: Part 9 : Bernouilli's Brachistochrone
10 Riemann for Anti-Dummies: Part 10 : Justice for the Catenary
11 Riemann for Anti-Dummies: Part 11 : Transcending Euclid
12 Riemann for Anti-Dummies: Part 12 : Gauss's Division of the Circle
13 Riemann for Anti-Dummies: Part 13 : The Finer Art of Science
14 Riemann for Anti-Dummies: Part 14 : The Dissonance that Smiled
15 Riemann for Anti-Dummies: Part 15 : The Solar System's Harmonic Twist
16 Riemann for Anti-Dummies: Part 16 : What's in a Moment?
17 Riemann for Anti-Dummies: Part 17 : Science is not Consensus
18 Riemann for Anti-Dummies: Part 18 : Doing the Impossible
19 Riemann for Anti-Dummies: Part 19 : The Known is Only a Special Case of the Unknown
20 Riemann for Anti-Dummies: Part 20 : Gauss' Attack on Deductive Thinking
21 Riemann for Anti-Dummies: Part 21 : It is Principles, Not Numbers that Count
22 Riemann for Anti-Dummies: Part 22: Your Education was Not Merely Incompetent
23 Riemann for Anti-Dummies: Part 23: The Civil Rights of Complex Numbers
24 Riemann for Anti-Dummies: Part 24 : Let There Be Light
25 Riemann for Anti-Dummies: Part 25 : Schiller and Gauss
26 Riemann for Anti-Dummies: Part 26 : Ideas Cast Shadows, Too
27 Riemann for Anti-Dummies: Part 27 : Gauss' Declaration of Independence
28 Riemann for Anti-Dummies: Part 28 : Bringing the Invisible to the Surface
29 Riemann for Anti-Dummies: Part 29 : The Crimes of Klein
30 Riemann for Anti-Dummies: Part 30 : The Powers of One
31 Riemann for Anti-Dummies: Part 31 : The Circle's Orbital Period
32 Riemann for Anti-Dummies: Part 32 : The Beginnings of Differential Geometry
33 Riemann for Anti-Dummies: Part 33 : Hyperbolic Functions - A Fugue Across 25 Centuries
34 Riemann for Anti-Dummies: Part 34 : Power and Curvature
35 Riemann for Anti-Dummies: Part 35 : Mind as a Power Generator
36 Riemann for Anti-Dummies: Part 36 : Transcendental Harmonics
37 Riemann for Anti-Dummies: Part 37 : The Domain of Possibility
38 Riemann for Anti-Dummies: Part 38 : You Are Not Impossible
39 Riemann for Anti-Dummies: Part 39
40 Riemann for Anti-Dummies: Part 40 : Cognitive Least Action
41 Riemann for Anti-Dummies: Part 41 : The Long Life of the Catenary
42 Riemann for Anti-Dummies: Part 42 : Archytus from the Standpoint of Cusa, Gauss, and Riemann
43 Riemann for Anti-Dummies: Part 43 : Isaac Newton: Godmother of Baby Boomer Bookkeeping
44 Riemann for Anti-Dummies: Part 44 : Principles and Powers
45 Riemann for Anti-Dummies: Part 45 : The Making of a Straight Line
46 Riemann for Anti-Dummies: Part 46 : Something is Rotten in the State of Geometry
47 Riemann for Anti-Dummies: Part 47 : Defeating I. Kant
48 Riemann for Anti-Dummies: Part 48 : Riemann's Roots
49 Riemann for Anti-Dummies: Part 49 : The Hidden History of the Complex Domain
50 Riemann for Anti-Dummies: Part 50 : The Geometry of Change
51 Riemann for Anti-Dummies: Part 51 : The Power of Number
52 Riemann for Anti-Dummies: Part 52 : Abelian Functions and the Difference Between Man and Beast
53 Riemann for Anti-Dummies: Part 53 : Look to the Potential
54 Riemann for Anti-Dummies: Part 54 : The Dramatic Power of Abelian Functions
55 Riemann for Anti-Dummies: Part 55 : What Are the Real Objects of Physical Science?
56 Riemann for Anti-Dummies: Part 56 : Riemannian Spherics
57 Riemann for Anti-Dummies: Part 57 : Pythagoras As Riemann Knew Him
58 Riemann for Anti-Dummies: Part 58 : Bernhard Riemann’s “Dirichlet’s Priniciple”
59 Riemann for Anti-Dummies: Part 59 : Think Infinitesimal
60 Riemann for Anti-Dummies: Part 60 : The Power To Change, Change
61 Riemann for Anti-Dummies: Part 61 : To What End Do We Study Riemann's Investigation of Abelian Functions?
62 Riemann for Anti-Dummies: Part 62 : On the Continuum of the Discontinuum
63 Riemann for Anti-Dummies: Part 63 : Dynamics not Mechanics
64 Riemann for Anti-Dummies: Part 64 : Hypergeometric Harmonics
65 Riemann for Anti-Dummies: Part 65 : On the 375th Anniversary of Kepler’s Passing
66 Riemann for Anti-Dummies: Part 66 : Gauss’s Arithmetic-Geometric Mean: A Matter of Precise Ambiguity
67 Riemann for Anti-Dummies: Part 67 : A View From The Top
68 Riemann for Anti-Dummies: Part 68 : An Insider’s Guide to the Universe
69 Riemann for Anti-Dummies: Part 69 : Change is All Ye Know On Earth -- And in Heaven