Chapter 15, Objective Processes
Reproducible Results
Arithmetic shows the main idea of objectivity. Namely, a result does not
depend on who or what performs a calculation, but only on the rules for
addition, multiplication, subtraction and division. Except perhaps for
round-off error, arithmetic results are repeatable and reproducible.
Recipes and rule-based processes, when carefully done, give results
independent of who obtains them. In this situation, the results cease to
be subjective — that is dependent on the person getting them – and they
depend only on the context. In this situation, the results are said to be
objective.
The main advantage of objective (rule-based) reason and processes is as
follows. Once we have agreed upon the rules and recipes and on the
evidence or ingredients to use, the results obtained are independent of
who or what obtains them. The result could be a number if we are doing
arithmetic. It could be a judgment or a conclusion if we are dealing with
people. It may be an action or product when operating a device or
machine.
Rule-based reason is ideal when or if you agree on the rules and
information employed. Disagreement on this, and the ensuing absence of
rules or information needed by them, represents a limit of rule-based
reason. Disagreement over what rules, if any, to apply makes conclusions
subjective – that is, dependent on who obtains them.
Objective reason and empirical processes both rely on the idea of
following previously stated recipes and guidelines, preferably ones that
have given good results in the past. Unfortunately, people singly or in
organizations are capable of repeating and reproducing bad or inferior
results as well. Still, for many problems, rules or recipes for their
solution may be known. The recipes provide solutions for problems that
other people have met and solved. These recipes and guidelines represent
the experience and the opinion of others, those who have investigated or
explored the problems before. In arithmetic, science and technology, this
knowledge (recipes, tricks, procedures) is represented by written or
verbal statements of rules, patterns and recipes which may work.
Search For Repeatable and Reproducible Methods
Departures From Objectivity
The ideal or goal of objectivity is represented in the legal system by
the idea of impartiality. Lawyers, juries and judges interpret evidence
and laws. One aim is to obtain impartial, objective verdicts of guilt or
innocence, and assignments of blame, damages and punishments.
Rules and laws are subject to geographic chances. In different countries,
we have different legal systems. Some are impartial. In these there is an
attempt to apply previously established rules and regulations
objectively. In other systems, the justice may be corrupted by bribes,
prejudice, etc. Even in the more-or-less impartial ones, laws and
regulations differ. So what is against a law or a regulation in one
location may be legal in another.
Laws, including commercial ones, often have a moral or religious basis.
Moral and religious ideas often define and differentiate groups. What is
considered polite, or inoffensive in one group, will be impolite or
offensive in others. Laws and regulations in legal systems reflect these
differences.
Laws and regulations are often, if not always, subject to human
interpretation. Commercial laws are intended to control or regulate
business. Laws may also define or remove previous obligations or
liabilities. The economic needs, self-interest and desires of people,
affect laws.
Lawmakers are further requested by interest groups to write laws in one
way or another. Each group readily accepts laws to control and restrict
the behavior of any other group but itself. Laws as they are being
formulated may be changed minutely to the benefit of one group or
another. All of us have different ideas of what is fair. Our laws
themselves are compromises between the views, principles and interests of
several groups, often satisfactory to none. So we cannot say in advance
that a set of laws will be complete and not contradictory.
Circumstances may occur to which the laws apply, but for which the rules
are not intended. Or unforeseen circumstances will occur to which the
laws do not directly apply. This points to the need for a new law or new
judgments about the application of existing laws. Human laws are human
creations. And humans individually or collectively may err. The
formulation of laws and rules and principles by people introduces the
possibility of error.
Postscript 2001-01-31 (Online Only): Rules and
regulations are written or drafted by clerks or civil servants in a
government under the direction of a cabinet minister. Most law makers,
following the direction of their parties, typically do NOT read in full
the laws and regulations they pass. In consequence, lawmakers do not
know their own intent in passing a rule. The precise interpretation of
an imprecise rule or law may be left to courts or judges. The latter
try to guess the "original" intent of the law. That is absurd. For
example, the fall 2000 US federal elections with it counting of votes
and voter intent in Florida according to ambiguous or inconsistent laws
and regulation provided an instance of this, and a court battle to
determine the US president.
Approximate Objectivity
Laws and regulations, however obtained, may be applied in an objective
manner. Objectivity may be subject to mitigating circumstances, political
interference, the ability of lawyers, the opinions or morals of judges,
etc. Results may vary or differ due to different laws and mores in
different locations — including your hometown; or due to ad hoc
departures from objective applications and interpretations of existing
laws and rules, however carefully written or not. But the ideal of
objectivity with human-made and human-applied regulation remains.
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Teachers & Tutors: Site pages offer better or best practices for providing skills -
simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in
groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do.
Others are welcome to refine or exceed it. Please do.
Secondary
Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges
with local curriculum control. Study how to include site content - its skill development how-TOs and innovations
into present or future lesson plans - some reading required.
Road
Safety Messages and Questions: When and why should you face
traffic when walking along a road or cycle path? Is it a good
idea to hang limbs outside of cars etc? What gives more
protection in a crash: a car, motorbike or bicycle?
See too, the BBC-Belgium story Texting and
Driving - texting & the impossible test - the article links to a gruesome utube video on the subject
The Logic of Injustice:
How Texas sent
an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for
justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning
first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon
due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions
by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate
is not compensation for years or decade
of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern
Based Reason may slowly lead to greater precision in reading, applying and
writing laws.
May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
Intellectual View, Feedback Welcome:
The 8 Most Popular Site Inlinks
Parent Center: Help your child or teen
learn:
Parent-friendly
Work Booklets for ages 3+ to 13 Use these or others to check
or build skills. Other booklets are available but these booklets
allow parents unsure of themselves in mathematics to help their
children. The selection acquired in Canada is published in the
USA. So it has a US orientation. In retrospect, the selection
shows parents what to check with the booklets or by other ways,
the choice is theirs. But in retrospect, the selection does not
cover integral and fractions liquid weights and measures - ask
the publishers to correct that! For ages 9 to 12 say, parents may
compensate by showing boys and girls how to use weights or mass,
and further measures in food preparation. Beyond that children
may be shown how to measure and calculate angles, lengths and
areas [proportional amounts too] directly or by using maps and
plans drawns to scale. Learning how to gather and measure all the
ingredients, pots and pans for a dish or a meal, along with
cleaning up sets the stage for like activities or experiments in
science courses, and in developing organizational skills,
gives boys and girls a head start. Good luck. At the other
extreme, more comprehensive than light, if your motto is
McCainian: drill, drill, drill then Toronto
mathematician and actor John Mighton's jump math organization has jump math
workbooks for at least grades 3 to 8 for at-home and in-school
use - training sessions for teachers available. Jump math has
been expanding to cover older students. Jump Math Samples: plus
Fractions for
Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8
[unread - likely to be good]. and
Mathematics
Skills For Ages 3 to 14 - technical!
Skills with take
home value - A few ideas
Basic skills include
time-date-calendar Matters; money matters; map, plan and
scale diagram matters;counting, measuring and figuring;
decision making with logic and likelyhood; being careful and
being aware of the domino effect of mistakes; reading and
writing with precision.
Is your child able to add, subtract and multiply amounts
of money, work with fractions, work with clocks and calendars,
work with maps and plans, and measure length, weight-mass and
volume? Schools may promote your son or daughter without
providing basic skills in reading, writing and
arithmetic.
Arithmetic
and Number Theory Skills
Algebra
Starter Lessons
Geometry
- maps plans trigonometry vectors
More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
-
How to Ace Calculus: Street Wise Guide - Mostly
Text.
-
Flash
Video for Calculus Phobics
They cover basic topics in ways likely to complement your
notes, your textbooks and site material. When Goldilocks
trespassed in the house of the three bears, she found three bowls
of porridge, two not to her liking, and one just right. Different
bears have different tastes. As invited guest here and elsewhere,
if one or more explanations is not to liking, try another. It may
be better or just right.
Unsolicited Advice
Learning to do and high marks if it comes to easy is often
deceptive - light rather than deep. For that reason, students
with learning difficulties determined not to let it get in their
way may go deeper and farther than those with none. High marks,
if the come easy, may be deceptive - provide a too light and not
a deep mastery. That could have been your problem in secondary
school, one that leads to comprehension shock or difficulties in
calculus and more generally in the first year of college. Bon
Appetite.
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