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YOU are better than YOU think. Show
yourself how:
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Logic
chapters 1 to 5 re- appear not in sequence, as is or longer,
in Volume 1A, Pattern Based
Reason, Bon Appetite.
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
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension. Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is approximately
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What may be learnt and when depends on how skills
and concepts are developed. Making the hard easier and clearer will allow
earlier & richer development of skills and concepts.
Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
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Details of the Scientific Method
Chapter 16
Previous: Rules, Reliable or
Not: - Scientific Method, Prediction, Testing, Correction)
Control and a Scientific Method
Reproducibility and repeatability form the basis of our daily technology. We
look for a regularity – a repeatable pattern. Then we rely on it. Moreover,
once a regularity is found, variations of it are tried in the hope of finding an
improvement. A reproducible event gives a situation which can be controlled and
then experimentally disturbed.
Inductive and Empirical Reason
The observation of regularity provides a basis for empirical, inductive
reason. Here patterns which appear to be reliable are extracted from experience
or trial and error. The use of these patterns in chains of reason then provides
examples of deductive reason. But uncertainty in the patterns cast doubt on the
conclusions obtained. Not all is certain, but some patterns appear to be
reliable. Confidence in them comes gradually.
Review Question – A Hint of the Contrapositive:
For a reliable rule which says that when a first situation occurs, so does a
second, what can you conclude when the second situation does not occur? (Hint:
See the first logic puzzle in the chapter Implication Rules or all of
chapter The Contrapositive to find the answer.)
A Scientific Approach to Cooking
In cooking and other situations, when we do not do anything differently,
nothing different results or nothing extraordinary results. The situation is
reproducible. When we modify some recipe, instruction or procedure, a new result
may be produced. We can be fairly sure that whatever we did or changed made the
new result appear. To be more confident of this, we could describe the
reproducible situation in writing and describe what happens with and without the
change. Then we could ask someone else to follow this description. If other
people can obtain the same result(s) as us, without further instruction from us,
the change we have made has caused [2] another repeatable
and reproducible process.
[2] There is an assumption here.
Controlled Situations & Exploratory Changes
When repetition of a sequence of actions leads to one result and no other, a
controllable situation has appeared. Again, this is like cooking. Following a
recipe carefully enough leads to the same result each time — the reproducible
meal. Further, after the recipe is seen to work, we can ask what happens if one
step in the recipe or sequence of actions is changed. This can lead to more
reproducible results (or reproducible disappointments or disasters). In this
manner desirable and not desirable recipes and implication rules for cooking can
be found and tested.
In the physical sciences and in technology, circumstances which can be
repeated and changed (perturbed) give opportunities for finding and
experimenting with reproducible results. Reproducible results are possible in
those controllable situations which almost repeat themselves, or can be repeated
by us. Rules which say what should happen in repeatable situations can be
tested. Just set up the situation (or wait for it). Then do your test.
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: Scientific Method - Reaction
to Failed Tests
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www.whyslopes.com
Volume 1A, Pattern Based Reason
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
To reason often means to persuade someone of
the need for an idea or action. That someone could be yourself. So be
careful.
Vol 1A Postscripts
- online only
+Proof by
Absurdity alias proof by contradiction
+How the demand
for consistency supports the law of the excluded middle
There is a difference between
knowing how to spend money,
and having money to spend.
There is likewise a difference
between mastering a skill
and having meeting a situation in which it applies.
.
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