Disclosure!

Christmas is a time of the unveiling of Celestial Beings. It is a season of epiphanies and manifestations. Some would call them "Extraterrestrials". Recently we shared some thoughts of John Wesley on the subject. Other notable Christians have also expressed their views:

Billy Graham:

“Some reputable scientists deny and others assert that UFOs do appear to people from time to time. Some scientists have reached the place where they think they can prove that these are possibly visitors from outer space. Some Christian writers have speculated that UFOs could very well be a part of God's angelic host who preside over the physical affairs of universal creation. While we cannot assert such a view with certainty, many people are now seeking some type of supernatural explanation for these phenomena. Nothing can hide the fact, however, that these unexplained events are occurring with greater frequency.” - Angels God's Secret Agents, p.21

Billy Graham ministered to many US Presidents notably President Richard Nixon. President Nixon reportedly confided to some, knowledge of ET life. One of these was Jackie Gleason http://www.openminds.tv/gleason-ets/. Had President Nixon confided to the evangelist too? We may never know but Billy Graham is correct saying "these unexplained events are occurring with greater frequency". Indeed, it is said these sightings have suddenly spiked since October 2010 and could increase into 2011. This week, New Zealand was the next in a series of countries to have declassified its UFO files http://www.nzherald.co.nz/politics/news/article.cfm?c_id=280&objectid=10695989. Yesterday Argentina announced the formation of a commission to investigate the UFO phenomenon http://www.examiner.com/exopolitics-in-seattle/breaking-news-argentine-air-force-announces-committee-to-study-ufo-phenomenon-1. Julian Assange of Wikileaks also indicated that among the US Diplomatic Cables now being posted. are references to UFOs http://www.examiner.com/ufo-in-canada/wikileaks-to-release-ufo-bomshell. Some are expecting more government disclosures soon.

CS Lewis:

"The dangers to be feared are not planetary but cosmic, or at least solar, and they are not temporal but eternal. More than this it would be unwise to say. ..... . . there would be indications enough in the narrative for the few readers - the very few - who at present were prepared to go further into the matter....What we need for the moment is not so much a body of belief as a body of people familiarized with certain ideas. If we could even effect in one per cent of our readers a change-over from the conception of Space to the conception of Heaven, we should have made a beginning." - Out of the Silent Planet

"The eldila are very different from any planetary creatures. Their physical organism, if organism it can be called, is quite unlike either the human or the Martian. They do not eat, breed, breathe, or suffer natural death, and to that extent resemble thinking minerals more than they resemble anything we should recognize as an animal. Though they appear on planets and may even seem to our senses to be sometimes resident in them, the precise spatial location of an eldil at any moment presents great problems. They themselves regard space (or “Deep Heaven”) as their true habitat, and the planets are to them not closed worlds but merely moving points - perhaps even interruptions - in what we know as the Solar System and they as the Field of Arbol." - Perelandra

Though Science Fiction, CS Lewis' Sci-Fi Trilogy, Out of the Silent Planet, Perelandra, and That Hideous Strength, like his Chronicles of Narnia helps the Christian to wrestle with the theological implications of our new cosmologies and planetary life. Lewis' interest in astronomy and the "idea of other planets" began as a young boy. "The idea of other planets exercised upon me a peculiar, heady attraction, which was quite different from any other of my literary interests." (Surprised by Joy, II)

Conclusion
We live with the questions. Graham and Lewis helps us, living in the "Space Age",  to reflect on such matters. Whether there will be any official disclosures in the very near future remains to be seen. At this Christmas time, however, more startling, the most astonishing of all possible disclosures, is the epiphany of the Christ child two-thousand years ago. No headline could be more amazing than that heralded by a Star to Astrologers from the East or that of a host of Celestial Beings "leaked" to Shepherds in fields watching their flocks by night. Billy Graham was correct in rebuking his close friend, President Richard Nixon, once when Nixon described the Apollo 11 mission as the "greatest week in the history of the world since Creation." It wasn't:

Let earth and Heav’n combine, Angels and men agree,

To praise in songs divine, Th’ incarnate Deity,

Our God contracted to a span, Our God contracted to a span,

Incomprehensibly made Man.

He laid His glory by, He wrapped Him in our clay;

Unmarked by human eye, The latent Godhead lay;

Infant of days He here became, Infant of days He here became,

And bore the mild Immanuel’s Name.

See in that Infant’s face, The depths of deity,

And labor while ye gaze, To sound the mystery

In vain; ye angels gaze no more, In vain; ye angels gaze no more,

But fall, and silently adore.

Unsearchable the love, That hath the Saviour brought;

The grace is far above, Of men or angels’ thought:

Suffice for us that God, we know, Suffice for us that God, we know,

Our God, is manifest below.

He deigns in flesh t’appear, Widest extremes to join;

To bring our vileness near, And make us all divine:

And we the life of God shall know, And we the life of God shall know,

For God is manifest below.

Made perfect first in love, And sanctified by grace,

We shall from earth remove, And see His glorious face:

His love shall then be fully showed, His love shall then be fully showed,

And man shall all be lost in God

- Charles Wesley

Books:

Christianity and UFOs

http://www.amazon.com/Christianity-and-UFOs/lm/R1ETCGCGITF223

Walter Hooper, C.S.Lewis, A Companion & Guide













Billy Graham, Angels God's Secret Agents













©Colin G Garvie HomePage: http://www.garvies.co.za

Factorials: A Christmas Postscript

I had just posted my previous blog about Kevin's fascination with factorials when Kevin's wife asked about the origins of the Christmas Carol, "The Twelve Days of Christmas", on Facebook. That was quite serendipitous...

Verse 12
On the twelfth day of Christmas,
My true love gave to me:
Twelve Drummers drumming,

Eleven pipers piping,

Ten lords-a-leaping,
Nine ladies dancing, Eight maids-a-milking,
Seven swans-a-swimming,
Six geese-a-laying,
FIVE GOLDEN RINGS!
Four calling birds,
Three french hens,
Two turtle doves
And a partridge in a pear tree.

Whether the carol was coded with Gnostic or Roman Catholic allusions didn't concern me that much. Instead the coincidence reminded me of the magic of Pascal's Triangle. (See http://dimacs.rutgers.edu/~judyann/LP/lessons/12.days.pascal.html.)

Pascal's Triangle

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

1 10 45 120 210 252 210 120 45 10 1

1 11 55 165 330 462 462 330 165 55 11 1

1 12 66 220 495 792 924 792 495 220 66 12 1

.

.

Pascal's Triangle is used for determining Probabilities, Combinations, and even Fibonacci Numbers. With the aid of Pascal's Triangle one can also: 

• find the number of new gifts given each day of "The 12 Days of Christmas.".
• the number gifts given on each consecutive day.
• the total number of gifts given by a particular day.

Embedded within the triangle of arithmetic data is useful information. Uncovering this detail evokes a sense of wonder, the same wonder scientists, poets, and exegetes experience when they "see" something more in the ordinary. Wonder is a moment of disclosure or revelation. We might call this process of discovery "mathematical deduction", "data processing", "the scientific method", "hermeneutics", or "exegesis" depending on the discipline we come from but the sense of satisfaction is the same. Contemplating Pascal's Triangle yields unexpected moments of surprise much as the thought that there's an oak within an acorn might.

With Twelve Drummers Drumming in my ears and Pascal's Triangle in my mind's eye, my Christmas thoughts turned to two fascinating Advent theological insights:

 The Logos

"And the Word (logos) was made flesh, and dwelt among us and we beheld His glory." (John 1:14) The Neo-Platonists and especially Philo used the word logos in a dual sense. For Plato and Philo the logos was the collective term for the Ideal World. The Divine Word contains within itself the archetypal forms of all things from which everything else is manifest, "made flesh", much as information leaps out at one from Pascal's Triangle. Philo spoke of the logos in a twofold sense (http://www.duke.edu/web/classics/grbs/FTexts/44/Kamesar.pdf):

i.  Logos endiathetos. This was the Transcendent Word, the Uncreated Template or Archetype.

ii. Logos prophorikos, the Manifest Word or created type.

"Some theologians distinguished between the logos endiathetos, or the Word latent in the Godhead from all eternity, and the logos prophorikos, uttered and becoming effective at the creation." (http://mb-soft.com/believe/text/logos.htm) In a symbolic way Pascal's Triangle (Logos endiathetos) embodies patterns that come to be manifest (Logos prophorikos), incarnated, or projected, and applied in the created world.

(Compare "Archetypes" and "Projection" in Jungian Psychology. For a helpful article on Philo and the distinction he made see http://www2.nd.edu/Departments/Maritain/etext/hhp49.htm. Also Wikipedia http://en.wikipedia.org/wiki/Logos. And Krishna in the Bhagavad Gita 9.)

Recapitulation

"Recapitulation" is the doctrine originally expressed by Irenaeus that all things are "summed up" in Jesus Christ. John Paul II explained: "God's saving plan, "the mystery of his will" (cf. Eph 1: 9) for every creature, is described in the Letter to the Ephesians with a distinctive term: to "recapitulate" all things in heaven and on earth in Christ (Eph 1: 10)...Irenaeus extols the one Lord, Jesus Christ, who in the Incarnation sums up in himself the entire history of salvation, humanity and all creation: "He, as the eternal King, recapitulates all things in himself" (Adversus Haereses, III, 21, 9)."  Theologically Christ is the Alpha and Omega of all Cosmic space and time. Another theologian, Julie James, wrote: "Irenaeus describes Humanity and God as coming together in Christ, an eventual restoration of the separated Human into the original divine form. Since the dawn of mans' entrance into the world, God has had a dialogue with humanity through the prophets, through his Divine Word, through rules and guidance, drawing mankind ultimately to the final goal of divinity, the Omega point." Irenaeus anticipates the Christogenesis of Teilhard de Chardin. Christ is the summation of all there is.....by analogy, the Divine Logarithm, the Beginning and the End. He encapsulates and recapitulates all. He is the "capstone".

oOo

Long ago, Magi from the East looked up into the night sky and were amazed by an astonishing configuration of the planets and stars. Suddenly it was pregnant with meaning just as Pascal's Triangle came to be for me. They discerned patterns hitherto never recognised before. Suddenly the ordinary took on a radical new import, wonder, and significance for them. The Divine was swaddled in a manger as revelations are swaddled in Pascal's Triangle. Immanuel! It could be a "partridge in a pear tree". It is the smile on an infant's face...

Still the night, holy the night!

Son of God, O how bright

Love is smiling from Thy face!

Strikes for us now the hour of grace!

©Colin G Garvie Home Page: http://www.garvies.co.za/

Ecstatically Factorial!

"Following in the way of the Ancients, we are in complete agreement with them in saying that, since there is no other approach to a knowledge of things divine than that of symbols, we cannot do better than use mathematical signs on account of their indestructible certitude."

-Nicholas of Cusa, Of Learned Ignorance, I.xi

Nowadays now that I am more prone to senior moments, a friend of mine speaks ecstatically about what I'll call "mathematical moments", moments when he's been raptured by the discovery of a new mathematical insight such as Mandelbrot Sets or the Golden Ratio. These are a cause of celebration for Kevin. Kevin becomes quite animated as he shares his story.

There was a young man from Trinity,

Who solved the square root of infinity.

While counting the digits,
He was seized by the fidgets,
Dropped science, and took up divinity.
                                 -Author Unknown

The other day Kevin shared one such exquisite moment when, in a flash of inexplicable insight, the elegance of factorials had dawned on him. For Kevin, it was a singular "red letter day" in his life. He cannot explain shy it should have affected him in such a profound way other than it seemed as if it was a moment in which the Universe fell into place for him. Something similar happened to me when once my lecturer in “Space Physics” remarked that the spiral was the key to creation. It was one of those rare "Aha!" moments.  Kevin admits he isn't even sure he fully understands what factorials are. Nor do I but he did get me to thinking that, if anything, such moments of awesome wonder might have something to do with the elegance and beauty of Factorials in particular and of Mathematics in general.

Davis and Hersh in their The Mathematical Experience explain that...

"The aesthetic appeal of mathematics, both in passive contemplation and in actual research pursuit, has been attested by many..." (p.168f)

Aristotle wrote:

"The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful." (Metaphysics, M 3, 1078 b)

Thomas Dubay says in his “have to read book”, The Evidential Power of Beauty, Science and Theology Meet, "...that mathematicians, at least the most alive of them, can burst into ecstatic joy over a newly discovered equation." (p.130)

Dirac went as far to say that it is more important to have beauty in one's equations than to have them fit the experiment! For some, such beauty might present itself in algebra. For others it could be the sublime theorems of Geometry. Trigonometry is the means of grace too. But for Kevin, it was Factorials.

The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions. ~Ronald L. Graham

What is a factorial? In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n.  (http://en.wikipedia.org/wiki/Factorial See also: http://en.wikipedia.org/wiki/Factorial_number_system)

For example:

1! =1x1 = 1

2! =2x1 = 2

3! =3x2x1 = 6

4! =4x3x2x1 = 24

5! = 5x4x3x2x1 = 120

6! = 6x 5x4x3x2x1 = 720

Or we could express it this way:

The factorial of 4 is 4 times the factorial of 3.

The factorial of 3 is 3 times the factorial of 2.

The factorial of 2 is 2 times the factorial of 1.

The factorial of 1 is 1 times the factorial of 0.

Or:

4! = 4 x 3!

3! = 3 x 2!

2! = 2 x 1!

1! = 1 x 0!

Cause and Effect. The one is the consequence of what has gone before. This is called "recursion". Each new term is generated by recalling a particular function that has gone before. The factorial of a number is that number multiplied by the factorial of the number before.  Though factorials and fractals are not to be confused the processes of recursion  and iteration are similar. Fractals are patterns within patterns within patterns. Factorials are numbers.

"Everything in the universe exists because of a cause and effect relationship. Any thing you wish to examine exists as an effect something else that existed before it. .....you get the regression going back. But as in all recursions, the regression must stop so later "things" can exist," explains one writer. 0! can be thought of as the First Principle or Primal Cause.

Factorials occur in many business, engineering, and science calculations such as in "permutations", "combinations", and "calculus" . For example, permutations or the possible number of rearrangements of objects in relation to each other has long amused the human mind.

Wikipedia again:

The rule to determine the number of permutations of n objects was known in Hindu culture at least as early as around 1150: the Lilavati by the Indian mathematician Bhaskara II contains a passage that translates to:

The product of multiplication of the arithmetical series beginning and increasing by unity and continued to the number of places, will be the variations of number with specific figures.

Or consider this example. This is so elegant...

....where e is the mysterious, transcendental number

e = 2.718281828459045235360287471352662497757247... ...

that can never be fully resolved.

Common or Briggian Logarithms are calculated to the base 10, Natural or Napier Logarithms are calculated to the base e.

Mathematics is akin to an icon, a window into a deeper mystical essence. It could even be sacramental in a way, a means of grace...an outward and visible sign of an inward and invisible grace. As Davis and Hersh remind us, mathematics is a fit subject for thoughtful contemplation. It has evoked wonder and bliss in the hearts of many. Mathematics is a symbolic representation of the Universe of which we are an integral part.

To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology. ~Hilda Phoebe Hudson

Oh! I almost forgot, by definition, 0! ≡ 1. Go figure!

For further reading:
1. HE Huntley, The Divine Proportion













2. PJ Davis & R Hersh, The Mathematical Experience















3. CC Clawson, Mathematical Mysteries, The Beauty and Magic of Numbers














4. T Dubay, The Evidential Power of Beauty

 
 
 
 
 
 
 
 
 
 
 
 
 
©Colin G Garvie HomePage: http://www.garvies.co.za/

The Cosmic Sea

When I was a kid I was assured that radio waves propagated itself through something illusive called the "Aether". I was told that...

"... the easiest way to break into the wireless game is to put up an aerial and hook up a receiving set to it; you can then listen-in and hear what is going on in the all-pervading ether around you, and you will soon find enough to make things highly entertaining... There is a strikingly close resemblance between sound waves and the way they are set up in the air by a mechanically vibrating body, such as a steel spring or a tuning fork, and electric waves and the way they are set up in the ether by a current oscillating in a circuit." (Frederick Collins, The Radio Amateur's Handbook, A Complete, Authentic and Informative Work on Wireless Telegraphy and Telephony).

I took that to be gospel even though way back in 1887 already, Michelson and Morley conducted experiments to detect the so-called "aether drift". They ruled out the existence of the aether. "This, in turn,", says controversial physicist, Ken Seto, "led to the erroneous conclusion that there was no substance of any kind occupying space." Subsequent experiments arrived at similar conclusions. Albert Einstein agreed. So, by the time I came to read Taylor and Wheeler's Spacetime Physics in 1965 I needed to unlearn the Doctrine of Aether from Collins' "authentic and informative work on wireless". The Aether was now but a figment of the imagination.

But then, in 1987 EW Silvertooth performed experiments with more sophisticated equipment and detected the existence of the Aether! (Experimental Detection of the Ether", Speculations in Science and Technology, Vol.10, No.1, page 3 (1987),   http://160.114.99.91/astrojan/silverto.pdf). I was in a quandary once again. It seems that Collins and my old wireless textbooks might be correct after all! Oh, the shifting sands of physics and theology.

I don't know with absolute certainty whether the Aether exists or not. I cannot say whether it can be measured or not. No doubt Heisenberg's “Uncertainty Principle” (http://en.wikipedia.org/wiki/Uncertainty_principle) applies here too. I don't know if Ken Seto is a "genius or a madman" (http://sci.tech-archive.net/Archive/sci.physics/2005-02/8496.html). I have no means of validating Silvertooth's conclusions. Does the Aether permeate all that is? We live with the questions. Whatever, this is a healthy reminder to me that even respected scientists can be at odds with each other. This also brought my attention to something more. It was South African philosopher-statesman, Jan Smuts, who suggested that we are much more than just the sum of our anatomical parts. There might be more to the Aether than meets the eye too.

Jan Smuts wrote in his Holism and Evolution....

"This whole is not an artificial result of its parts; there is something more than the parts, and this something appears to be in definite relation with them, influenced by them and again influencing them... "

(From Holism and Evolution, p.78)

In another remarkable passage Smuts wrote:

"For we are indeed one with Nature, her genetic fibres run through all our being, our physical organs connect us with millions of years of her history; our minds are full of immemorial paths of pre-human experience.

"Our ear for music, our eye for art carry us back to the early beginnings of animal life on this globe. Press but a button in our brain and the gaunt spectres of the dim forgotten past rise once more before us; the ghostly dreaded forms of the primeval Fear loom before us and we tremble all over with inexplicable fright. And then again some distant sound, some call of bird or smell of wild plants, or some sunrise or sunset glow in the distant clouds, some mixture of light and shade on the mountains may suddenly throw an unearthly spell over the spirit, lead it forth from the deep chambers and set it panting and wondering with inexpressible emotion. For the overwrought mind there is no peace like nature's, for the wounded spirit there is no healing like hers. There are indeed times when human companionship becomes unbearable, and we fly to nature for that silent sympathy and communion which she alone can give.

"Some of the deepest emotional experiences of my life have come to me on the many nights I have spent under the open African sky, and I am sure my case has not been singular in this respect.

"The intimate rapport with nature is one of the most precious things in life. Nature is indeed very close to us; sometimes closer than hands and feet, of which in truth she is but the extension. The emotional appeal of nature is tremendous, sometimes almost more than one can bear."

(From Holism and Evolution, p.336f)

Intuitively we know we are part of, even integral, to a greater whole. By some mysterious ethereal thread we are spiritually connected to all space and all time. Mystics and Scientists testify to this. Gregg Braden writes about the "Divine Matrix". Paul said something similar to the Greeks, "For in Him we live, and move, and have our being; as also certain of your own poets have said, `For we are also His offspring.'" (Act 17:28).

Eager for Thee I ask and pant;
So strong, the principle divine
Carries me out, with sweet constraint,
Till all my hallowed soul is Thine;
Plunged in the Godhead's deepest sea,
And lost in Thine immensity.
            - Charles Wesley, MHB 299



©Colin G Garvie HomePage: http://www.garvies.co.za/