Appetizers and Lessons for Mathematics and Reason   
www.whyslopes.com          ( Français
 Logic mastery is key to easing or avoiding learning difficulties in work & studies. 

Online Volumes (Book Orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3.
Why Slopes & More Math 1995

Site  Folders for Instructors & Adults
A. Public Policy Essays
B.  Mathematics  Education Essays  2006-7
C -Logic & Applied Math Program  
    for education,  June 22, 2008 
D. Quebec English Math Ed -  Standards to
 avoid  in course design & teacher education 
E. Help your child or teen
How TOs/ Ref.-08- 2008
1. Arithmetic Reference
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus
7. Logics in Maths
16 Chaos      Back ] Up ] Next ]


Pattern
Based
Reason

understanding & explaining
Reason and Math
Volume 1A
Printed in Canada
ISBN 0-9697564-5-3

To reason often means to persuade someone of the need for an idea or action. That someone could be yourself. So be careful.

Learn More: If  this work  is too your liking, you may also like the foreword of Volume 1, Elements of Reason. with its description of all site volumes. 


YOU are better than YOU think. Show yourself  how:

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 For better work & study skills, read logic chapters 1 to 5  in  Three Skills for Algebra. Sooner is better. Good luck.

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 Logic Mastery
 Amazing, Amusing, Amorous,  Delicious, Delightful, Edifying, Strengthening Elixir. 
It eases work & learning difficulties. Makes the hard easier. Opens eyes. Leads to greater precision.
in reading and writing

Do not leave here without it -  Logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.


Explore collaborative whiteboards from groupboardtwiddla  or scriblink.


Chaos
Chapter 16

Previous: Scientific Method - Reaction to Failed Tests

Chaotic situations make observation and pattern spotting difficult, perhaps impossible. In situations which cannot be controlled, there is no observable normal or stable state of affairs to which the system returns after any disturbances. In such situations, reproducibility of results is not seen. There is too much movement for any stable pattern to emerge. Each situation is not repeated nor seen again by an observer.

Knowledge is most certain in dealing with machines and bureaucracies where behavior is repetitive, controllable and reproducible. The rules for their operation are firm and rigid. Less certain knowledge appears in uncontrollable, and non-reproducible situations. Think of economics or weather systems. These are examples of uncontrollable circumstances. Rules describing their behavior may never be found.

What can we do in uncontrollable irreproducible situations? The answer perhaps is to look for patterns. These may provide some control. Chaos is reduced each time a reliable pattern is spotted and confirmed.


Chapter Sections: 16 Private Agreements ] 16 Public Laws ] 16 Physical Laws ] 16 Accidental Patterns ] 16 Reliable(?) Patterns ] 16 Scientific Method ] 16 Reaction to Failed Tests ] [ 16 Chaos ] 16 Statistical Inference ] 16 End Notes ]

Next: Statistical Inference and It Limitations

 


Foreword +  Chapters 1 to 24

FOREWORD
Three Remarks

1 Introduction
2 Communication
3. Elements of Reason
4 Implication Rules
5. Deception
6 Chains of Reason
7 Longer Chains
For & From Consistency
8. Language Change
9 Next Chapters
10 Responsibility
11 Accidental Patterns
12 Knowledge Islands
13 Euclidean Logic
14 Deductive & Empirical 
     Views of Mathematics

15 Objectivity
16 Origin of Rules
and Patterns
17 Objective Ways

18. Waking up
19. Symbols  & Logic
20. Pronouns or Symbols
21. Truth Tables I.
22. Truth Tables II
22. Biconditional
22. Contrapositive
23. IF-THEN table
24. Indirect Reason Again

1A Logic Postscripts
- online only

+Proof by Absurdity alias proof by contradiction
+How the demand for consistency supports the law of the excluded middle
+Reality versus or with the aid of Imagination
+Links for reason, logic and crtical thinking
+Three Remarks
+History Lost or Missing

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Caution: Site advice is approximately correct, for some circumstances, not all. Site How-TOs are logically developed, but not tried and tested. That leaves room for thought and refinement..

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