Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Generalization of the Golden Rule
Replies: 0

 Ronald Brady Posts: 11 Registered: 8/21/09
Generalization of the Golden Rule
Posted: Jun 5, 2013 6:39 PM

Generalized Golden Rule (for Sci.Math)
It is well known that Newton?s Third Law of motion may be stated as follows: to every action there is an equal and opposite reaction. The Golden Rule, on the other hand, states that a person should do unto others as he would have others to do unto him. Actually the following is an equivalent re-statement of the Golden Rule: act in relationship to others as you would have them to react unto you.
*
Newton?s Third Law is a fundamental law of nature that applies to all macroscopic scale objects irrespectively of whether they are animate or not. Rushworth Kidder (Ref.1), founder of the Institute of Global Ethics, stated that the conceptual framework of the golden rule has appeared in many of the prominent religions of the world (Ref.2). These religions (including Christianity) teach that the faithful should voluntarily adopt the golden rule as a fundamental standard of ethics.
*
The Golden Rule is a religious principle that is endowed with the property of symmetry. Symmetry occurs throughout all the fields of science-especially in physics. In particular, it should be noted that ?Newton's third law is one of the fundamental symmetry principles of the universe.? (Ref.3, p.5)
*
In this paper we will propose that the Golden Rule and Newton?s Third Law be combined into a postulated generalized symmetry principle of nature such that if it is obeyed, then a state of equilibrium and symmetry will be the result.
*
Postulate (or conjecture) of the Generalized Golden Principle of Nature (GGPN)
If for every action, of an animate or inanimate entity in a physical and/or sociological system, there is an equal and opposite reaction in that system, then the result is that the system will exist in a state of physical and/or social equilibrium.
*
Proof (outline)
This is automatically true for strictly physical systems (including the physical bodies of all animate entities) as a consequence of Newton?s third law. To wit: let F denote the internal force that one part of an isolated body exerts upon another part of that body. And let ?F denote the reactive force that the second part of the isolated body exerts upon the first. Then the net force (F + (-F)), associated with the (internal) interaction, is equal to zero. It will be recalled, from high school physics, that when the net force acting upon an object is zero then the object is in a state of equilibrium and has no acceleration, [(Ref. 4a), (Ref. 4b)]
*
Now let?s outline the proof for special cases involving human beings. The author is well aware of the immensity and complexity of the structure of the set of interactions among members of the human family. But it is herein conjectured that human interactions at a fundamental level can be described by an analysis of sets of interactions that each involves only two human beings. For now let?s restrict our attention to economic interactions that involve the buying and selling of only a single product.
*
Let the members of a set S of human beings individually adopt the golden rule. Let person x and person y be any two arbitrary members of the set. Let the expectation of x be that, at time t, any other member of S, who is in the market to buy or sell a unit of product Q, will buy it from or sell it to x at the equilibrium market price of p(t). Assume also that person y has a similar expectation and that the equilibrium price p(t), for product Q, is known to all members of the set S for all times t.
*
Then if one of x and y is in the market to buy and the other is in the market to sell units of product Q and if they should meet in the market place for product Q at time t, then their mutual expectation will be that a unit of Q will be exchanged between them at a price p(t). And since they are both living in accordance with the principles of the golden rule, the product will be exchanged at the equilibrium price of p(t). And since the transaction will have been made at the equilibrium price, both persons x and y will be satisfied and will reside in a state of equilibrium with respect to the transaction(s) involving product Q at a unit price of p(t).
*
Symmetry
The present author is fond of making the claim that the equal sign is the most important symbol in math. One good way to overcome sex and/or race based discrimination in the work place is by acquiring a good knowledge of math. That can start with a good understanding of how the equal sign is used. So then a thorough understanding of the role of the equal sign in math can help to bring equal employment opportunity.
The equal sign (=) is endowed with the property of symmetry: that is expressed by the fact that if x = y then y = x.
A good knowledge of math will direct your path to a very successful career, whether as a doctor, lawyer or electrical engineer?..
RHB
Bountiful examples of symmetry occur in all branches of physics. We have already mentioned the symmetry principles associated with Newton?s Third Law.
*
One of the leading authorities on symmetry in theoretical physics, during the early part of the 20th century, was initially not allowed to teach in a paid capacity. The German Jewish math genius was not discriminated against because of religion but because of her sex. Emmy Noether ?was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics.? (Ref. 5)
An ?equality relation? (as in an equation) is a special case of an equivalence relation. Equivalence relations are studied in abstract algebra: a subject that Noether excelled in. For example, one could write the simple equation
*
Six = a half dozen
*
Each side of this equation is quantitatively equal to the other. On the other hand one cannot correctly write an equation stating the equality of apples and oranges. But one could very well state that apples and oranges are equivalently important in nutritional value. One cannot be certain but it is difficult to believe, that if Noether were alive today, she would disagree with the following:
*
Let the phrase ?do naturally? mean the same as ?do without high tech artificial aids or equipment?.
Let W be the set of jobs that women (on the average) tend to do naturally better than men. Let M be the set of jobs that men (on the average) tend to do naturally better than women. Let S be the set of jobs that both men and women (on the average) tend to do naturally equally well. Then the sets W and M are equivalent in importance to the preservation and continuation of human civilization. It is the firm opinion of the present author, who has taught both high school and college math, that the job of mathematician is a job that belongs to the set S (as defined above). Hopefully, women?s groups will start to give Noether, a gifted mathematician of the past, her proper due.
*
References
1.) Wikipedia
http://en.wikipedia.org/wiki/Rushworth_Kidder
Retrieved on 4-29-13
2.) Wikipedia
http://en.wikipedia.org/wiki/Golden_Rule
Retrieved on 4-29-13
3.) http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html
Retrieved on 5-5-13
4a.) Newton's Third Law
http://hyperphysics.phy-astr.gsu.edu/%E2%80%8Chbase/newt.html
Retrieved on 6-2-13
4b.) ?Calculating Equilibrium Where the Net Force on an Object Is Zero?
http://www.dummies.com/how-to/content/calculating-equilibrium-where-the-net-force-on-an-.html
5.) Emmy Noether: Wikipedia
https://en.wikipedia.org/wiki/Emmy_Noether
Retrieved on 6-1-13