Wow – eight years!

I neglected to mention that Saturday, 5/25 was the day in 2005 which saw the beginnings of this blogg.

It's hard to believe that so many years, almost a quarter of a billion seconds, have gone into the past, and this odd little electronic newspaper of mine has continued, with its faint glimpses into Chesterton or Jaki or mathematics or other curiosities. And in that time I have written almost 3000 pages of new fiction, most of which is now available in print. I won't state the number of lines of code I've written, nor the pages of non-fiction - but there's been some of those also, including an extension of a certain string-searching algorithm, an investigation into certain odd graphs, notes on pedagogy and science, on St. Paul's Analogy of the Body, and on other matters... but more on those another time. Besides, anyone can write such things, but not everybody can write stories. As GKC pointed out:

...a story is exciting because it has in it so strong an element of will, of what theology calls free will. You cannot finish a sum how you like. But you can finish a story how you like. When somebody discovered the Differential Calculus there was only one Differential Calculus he could discover. But when Shakespeare killed Romeo he might have married him to Juliet's old nurse if he had felt inclined.
[GKC Orthodoxy CW1:342]

And, yes, I thank God, I can write stories, and have people kill or be killed, marry or be given in marriage – or enter religious life – as I please. I can do Calculus too, and it's fun like automata theory, software design, and programming is fun, but sometimes I feel inclined to derive my fun in another way. Like floating tea-trays, or newspaper broadsides of 50,411 apparently random letters, or genius mathematicians who invent «unbreakable codes», or bells that hang in the tower of a college chapel: bells with mysterious properties...

One of the most significant lines ever written by the great J. R. R. Tolkien was in his preface to his trilogy, where he noted that he received only one complaint about it: "They invariably tell me it is TOO SHORT." I am NOT comparing myself to him; I do not dare. But I have encountered a similar difficulty with my readers. Yes, people have dared read the Saga, and they are enjoying it. (I enjoy it too, but then I had to read it or no one else ever could. Somebody has to do the hard jobs.)

Yes, the Saga, De Bellis Stellarum. Those eight years have seen its development, with its pleasant and homely vignettes of life in the famous American seaside booktown called Quayment, the recounting of the story of Joe Outis and how he started work in the famous Control Room of AC&TG, his involvement in the 2001 wreck of the Phosploion, the mysteries of Howell College, the Order, the College, the Inner Circle, and related topics... And, even more amazing, the foundation of that outstanding institute of Higher Learning, the Ambrosian University in Milan, Pennsylvania. There are some scholars who know about Cardinal Newman and how the Pope told him to establish a new University in Ireland: and how he studied the Idea of a University and presented a series of lectures (later a book) about his studies. Newman's university failed, though not because OF Newman; DESPITE Newman - and I might mention others who have had that experience. Yet he succeeded in another way, because his work persists, revealing important truths about the Idea of a University.

But as lowly and as unimportant as I am, I have discovered something Newman did not discover. It is, of course, due to my having read that "far too short" trilogy by Tolkien, and another important book of that sort called The Never-Ending Story by Michael Ende. I discovered that I was able to found a university, and give it something which Newman could not give: even if everyone from the Pope and the government to the faculty and students had supported him in his efforts, simply because it was ultra vires, beyond his ability to grant.

Yes: I founded the Ambrosian, as I founded Howell College and Collins University and others you will learn about in the Saga. But in founding them, I gave them not only their campus, their faculty, their entire curriculum, their libraries and all related properties: I also gave them the priceless gift of their HISTORY...

This is no self-deification; indeed, emphatically NO! This is nothing other than the gift of Subcreation. Believe me, it does not exalt at all; it is quite a humbling experience, just as being the architect of an important major 24/7 cable TV system is humbling: one becomes RESPONSIBLE to one's subcreated world. As you may know from Ende's masterwork, Bastian Bux enters into the Story; in that fantasy reality he wishes something into existence: and he is told from that moment, it has ALWAYS existed, and what he does with it matters in essential ways... Maybe a Sayers, a Chesterton, an Aquinas or a Gilson could explain this formally; but it is not necessary. When you pick up a pebble and let it drop, the pebble does not need to study Differential Calculus in order to know how to fall with constant acceleration... Or, as a friend of mine has stated, (I paraphrase here) a river is not intelligent because it adds its volume of water to the ocean. Of course, since God made the pebble and the river that way; they have those properties as part of their being. Well, God made us in His image, the image of a Creator, and we continue to exert those properties too. Therefore I ask: may God aid me as I proceed, wielding this most wonderful set of keys to unlock more and more doors to the Real World – even those labelled "Quayment" and "The Ambrosian" and so on.

The Great Novena Begins! (and a little piece of math news)

Today we begin the Great Novena to the Holy Spirit, the nine days of that most wonderful countdown to Pentecost. Please pray ferently, we need God's help so much!

Also, I was cranking over a curious recurrence function (more on that another day), and found that I required to know the closed form of the SUM of 3^i (that is, 3-to-the-i) for i running from 0 to n. No doubt you already know the formula, or have a handy book to find it, but I was dumb, and had to work it out for myself.

That is, I wanted T(n) = 1 + 3 + 9 + 27 + ... + 3^n.

Just to be clear, I will write out the first few results:

For n=0 T(0) = 1
For n=1 T(1) = 1 + 3 = 4
For n=2 T(2) = 1 + 3 + 9 = 13
For n=3 T(3) = 1 + 3 + 9 + 27 = 40
For n=4 T(4) = 1 + 3 + 9 + 27 + 81 = 121
For n=5 T(5) = 1 + 3 + 9 + 27 + 81 + 243 = 364

All right... it's obvious, right? The closed form is:
T(n) = (3^(n+1)–1)/2.

The proof is quite easy, and I will leave it to the reader. If you want to see it, let me know.

It reminds me of that hilarious thing we heard long ago, when I was in grad school, about a doll that squawked "Math is Hard!" and how I found out that Aquinas showed the CONTRARY, that Math is actually EASY. Oh yes. But that refers to the DISCIPLINE IN ITSELF, not to how one may find it at any given moment, especially when one has teachers who detest the subect. What a shame. Mathematics does have hard parts, but it can be a lot of fun, and of course every time we say its name we ought to recall our Lord's final words, "Go therefore and MAKE DISCIPLES OF all nations..." (Matthew 28:18) The Greek of course is πορευθέντες οὖν μαθητεύσατε πάντα τὰ ἔθνη, and there we see the root of MATHEMATICS (= The Learning): yes, to learn is to be a disciple. Let us keep that in mind during the Great Novena!

Lord Holy Spirit, enlighten us, in mathematics, and in all our studies, in all our work, in all we do... Amen.