Outline - The Spiritual Significance of the Square Root of Minus One

1. Introductory passages Luke 12:54ff

I Corinthians 14:20

Matthew 13: 52

2. Jesus’ parables illustrate the strong connection between the physical world and the world of mind and spirit. Parallel reasoning (rationality) in the two realms can be expected.

3. Many great discoveries about the universe and the physical world have been made since Jesus’ time - this presents great new opportunities for exploring and understanding both physical and spiritual phenomena, for bringing out treasures both new and old.

4. The problem of compartmentalization of human activity and thought.

5. The problem of the frequent de-emphasis in the Christian community of the importance of the mind.

6. Four assumptions - axioms

A. the universe is rational

B. our minds, created in the image of God, are meant to be used

C. there are two major sources of revelation

i. the book of “nature”

ii. the historical revelation to the people of God in holy history recorded in Scripture

D. some form of revelation is involved in all knowledge including scientific knowledge

7. Two interconnected illustrations of the linkage between physical, mental and spiritual:

(a) the root of minus one - a new kind of number

(b) the Schrodinger equation

8. Conclusion - there are strong linkages, parallels, unities between the physical, material world, and the world of mind and of spirit. These linkages can point to new insights and understandings of both old and new themes in human life and thought and in spiritual realities and dynamics.

9. What does this mean?

(a) conclusion above

(b) the importance of the doctrine of the resurrection from the dead

(c) there is much mystery in the universe, not because it is irrational, but because we are not God, and there are many things we don’t know and may be many dimensions we are not aware of

(d) our grasp spiritual realities may be more fully realized by finding parallels in the physical universe

(e) the wave-particle nature of natural phenomena such as light may help us to understand more fully why there has been so much unresolved attention given to issues such as freewill versus determinism

(f) we should approach understanding of all dimensions of the universe with both confidence and humility

(g) when we come to discover the fullest truth about all aspects of the universe (physical, emotive, mental, spiritual) we will most certainly find it surprising - the history of scientific discovery could not underline this more strongly.

Formulas, Numbers and Equations

Equations are used frequently and with great success in both mathematics and the application of mathematics to the physical world.

F = ma E = mc Work = Fd

Every equation has some solution - some number or value which makes the equation true. Take some examples:

x - 1 = 0 Solution =

(this is a natural number - it can be counted on your fingers)

x + 1 = 0 Solution =

( this number is not so natural - a negative number)

x - 1 = 0 Solutions =

(solutions are a mixture of natural and negative numbers)

x + 1 = 0 Solutions =

(this is now a very strange kind of number - it solves the equation but is not real)

i = and i = - 1

Why would anyone wish to have such a number? It may be interesting but quite useless and maybe even appears irrational. But it is very interesting that many mathematical discoveries have been made which at the time had no usefulness or practical application. But somewhere along the line it was discovered that it had a very practical and profound application. i - the square root of minus one is no exception. Look at the following equaton:

Total energy = Kinetic energy + Potential energy

of electron

This is the fundamental equation of quantum physics - one of the strangest but yet one of the most successful scientific theories ever derived. There has been no experiment yet that has called it into question. This is the equation that describes how electrons and other particles behave - it is at the heart of understanding how the atoms are held together in our bodies and the chemical processes that make them work - and at the heart of maybe even understanding why we have bodies.

Notice what’s there - the square root of minus one! Is that irrational? Not at all - quite the contrary - the equation was derived from quite rational processes - it may be counter - intuitive but it is not counter - rational.

The Concepts of Rationality

Reasoning involves the use of the human mind in thinking thoughts and drawing conclusions that are consistent , logical and objectively acceptable.

There are two kinds of reasoning:

A. Deductive reasoning - begins with an axiom or a premise or an established truth and from that base, by very clearly understood and objective rules of logic, reaches new conclusions or truths.

Two things may go wrong in deductive reasoning which may lead to erroneous conclusions:

- a process of deduction may be completely logical and consistent but may still end in a wrong conclusion because of wrong or questionable premises.

- deduction may begin on a sound basis with good and acceptable premises but go astray in the logic

Good deductive reasoning must depend on the soundness of both the premises and of the logical process.

B. Inductive reasoning - begins with careful observations of the world about us and issues in an hypothesis about the connections that may exist among the things observed. The person who reasons then conducts tests or experiments to either confirm, deny or modify the original hypothesis. If necessary a new or modified hypothesis is proposed which in turn is tested for validity. The process can be repeated as long as necessary to reach a valid conclusion. Any hypothesis, however, is always subject to further testing and modification.

Good inductive reasoning depends on the accuracy of the observations, the care with which the testing process is done and the extent to which the results can be repeated or tested by anyone anywhere.

Most scientific discovery and knowledge is based on the inductive process.

It is noteworthy that inductive reasoning can never produce absolute proof of anything, only strong evidence for a given conclusion. It is also true that deductive reasoning cannot provide absolute proof of anything because it must always begin with some unproved axiom or premise.

For example in the very objective pursuit of scientific knowledge we must make several very important but unproved assumptions:

- there are physical laws and these laws are always constant

- laws of physics are the same at all places in the universe - astrophysics impossible without this assumption

- the laws that operate today are the same as those that operated in the near and distant past

- the simplest explanation of any phenomenon is the best - most predictive

Although these are assumptions only there seems to be a lot of circumstantial evidence to support them. Nevertheless they remain beyond the reach of proof. (They must come to us in some form of “insight” or “revelation.”)

Thus reasoning, in and of itself, cannot ultimately lead us to absolute certainty about its objects of investigation. It can, however, provide results in which we can have a relatively high level of confidence.