Website owner: James Miller
MODERN, ABSTRACT MATHEMATICS
The modern mathematics that has come into vogue in the last hundred years or so is distinctly different from the classical mathematics of previous centuries. It is characterized by a very different approach, a different way of thinking, and by an abstractness that sets it apart from classical mathematics. It is a mathematics based on an axiomatic approach: Concepts such as a group, ring or linear space are defined in terms of a set of axioms or postulates. One then proceeds to figure out just how much follows logically from the stated axioms, just as in Euclidean geometry one starts with a stated set of axioms and logically deduces an entire body of theorems that follow logically from that stated set of axioms. The general procedure is indeed essentially the same as that of Euclidean geometry but there is a big difference. In Euclidean geometry one deals with figures in space that can be visualized. He is dealing with objects that are relatively concrete. Intuition plays a big role. Modern mathematics applies the Euclidean geometry technique of logical deduction from a set of axioms to abstract algebraic structures. As a consequence the reasoning and results tend be distinguished by great abstractness. The beginning set of axioms are generally stated in very abstract terms and on first sight one is likely to have difficulty figuring out what their real meaning might be. On first encounter they generally sound like gobbledegook. Generally they consist of a statement of a list of abstract properties or laws of some concrete system that one may not be familiar with. And the statement of the axioms themselves give no hint of what that concrete system might be. They may seem intellectually impenetrable. Generally there is some concrete model behind them that the creator of the axioms had in mind when he created them. For example, in the case of a linear space it is the vector space of three dimensions. In the case of a group the concrete model is the permutation group. In spite of the great abstractness and abstruseness of modern mathematics it can't be denied that there is a lot of power in the method. It can be surprising how much can be deduced from a small set of axioms. Profound results can be deduced. A good example is group theory. The discovery of quotient groups is a profound result deduced directly from the simple axioms for a group.
The Way of Truth and Life
God's message to the world
Jesus Christ and His Teachings
Words of Wisdom
Way of enlightenment, wisdom, and understanding
Way of true Christianity
America, a corrupt, depraved, shameless country
On integrity and the lack of it
The test of a person's Christianity is what he is
Who will go to heaven?
The superior person
On faith and works
Ninety five percent of the problems that most people have come from personal foolishness
Liberalism, socialism and the modern welfare state
The desire to harm, a motivation for conduct
The teaching is:
On modern intellectualism
On Self-sufficient Country Living, Homesteading
Principles for Living Life
Topically Arranged Proverbs, Precepts, Quotations. Common Sayings. Poor Richard's Almanac.
America has lost her way
The really big sins
Theory on the Formation of Character
You are what you eat
People are like radio tuners --- they pick out and listen to one wavelength and ignore the rest
Cause of Character Traits --- According to Aristotle
These things go together
We are what we eat --- living under the discipline of a diet
Avoiding problems and trouble in life
Role of habit in formation of character
The True Christian
What is true Christianity?
Personal attributes of the true Christian
What determines a person's character?
Love of God and love of virtue are closely united
Walking a solitary road
Intellectual disparities among people and the power in good habits
Tools of Satan. Tactics and Tricks used by the Devil.
On responding to wrongs
Real Christian Faith
The Natural Way -- The Unnatural Way
Wisdom, Reason and Virtue are closely related
Knowledge is one thing, wisdom is another
My views on Christianity in America
The most important thing in life is understanding
Sizing up people
We are all examples --- for good or for bad
Television --- spiritual poison
The Prime Mover that decides "What We Are"
Where do our outlooks, attitudes and values come from?
Sin is serious business. The punishment for it is real. Hell is real.
Self-imposed discipline and regimentation
Achieving happiness in life --- a matter of the right strategies
Self-control, self-restraint, self-discipline basic to so much in life
We are our habits
What creates moral character?