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.

Fiftieth Anniversary of Subsidiarity!

Are you surprised? Well, if you want to know more, see here for details.

And then let the party begin!

A cake would be suitable, and maybe some of the food we see at the banquet Jethro threw for Moses in "Ten Commandments", since it was Jethro's idea in the first place.

And if you are wondering what that odd picture is, and curious as to how cable television and satellite dishes like this onerelate to Subsidiarity, you ought to check out the book where it is explained - and Jethro too!.

Thursday in the Octave

Alleluia! "The splendor of Christ risen from the dead has shone upon the people redeemed by His blood, alleluia!"

It has surely been a very long time since I had posting on a Thursday. (ahem!) But this is no time for me to be writing on bloggs, not when I have so many other things waiting for me to handle. So I shall merely give you a brief taste of Chesterton on Easter, since it appears that people are hunting for such references. Please resume eating your chocolates and other goodies, and continue to rejoice - for OUR GOD KNOWS THE WAY OUT OF THE GRAVE. Amen. Alleluia!

...will be noted that where there is tea, there is tea-time. Where it really exists as a beverage that can be drunk, it also exists as an institution that must be observed; and the name of it is not merely tea, but afternoon tea. This element of concentration in time as well as space reappears, as everywhere else in the human story. A certain stage in the slow descent of the sun, a certain line in the mathematical map of heaven that is traced in stars, a certain fine shade between afternoon and evening, is made and marked by the ancient human instinct even for the modern institution of tea. Tea is a libation to the sun in that quarter of heaven, to the gods of that condition of earth and sky, fully as much as Easter eggs are proper to Easter or Christmas puddings to Christmas. It is true that by the necessities of the case it has to vary somewhat with the seasons; and it will be found that the institution takes on a slightly different tone in consequence. In that respect it resembles rather Easter than Christmas, and marks what is, in this merely light and local sense, the practical advantage of Christmas over Easter. Christmas is, quite apart from all its really important elements, the central and supreme example of this idea of concentration and fixity; because it is not a movable feast. Many excessive schools of lunatics have tried in vain to move it, and even to move it away. In spite of all sorts of intellectual irritations and pedantic explaining away, human beings will almost certainly go on observing this winter feast in some fashion. If it is for them only a winter feast, they will be found celebrating it with winter sports. If it is for them only a heathen feast, they will keep it as the heathens do. But the great majority of them will go on observing forms that cannot be so explained; they will keep Christmas Day with Christmas gifts and Christmas benedictions; they will continue to do it; and some day suddenly they will wake up nd discover why.
[GKC ILN Jan 3 1925 CW33:478]

Ahem... I must here intrude. The following is almost unsettling in its relevance to today - I have quite recently encountered some otherwise decent young people with college degrees who have never had courses in the basic theories underlying their disciplines - and that is horrifying, for that means they cannot appeal to first principles in any thing they may do... But GKC addresses the matter far better, and gives not only the solution, but reminds of of how Easter is part of that solution. But read it for yourself:

I believe a new and enormous number of people now have no opinions at all. Some have open minds; some have empty minds; but few have the positive and partisan opinions that prevailed in my boyhood. A few have convictions - indeed, there is some reasonable hope that the passing of opinions may be the coming of convictions. But most people have not yet got the convictions and have already lost the opinions.... In some ways it may well be said that this blank state of mind is a better thing than the bigotries and blatant slanders of the past. And up to a point, doubtless, it is a good thing. But there is a further difficulty which I do not think is very well understood. Not only have men lost their opinions, but many of them seem to have lost the power of forming opinions. They have seen all there is to be seen of the last stages of beliefs; but they do not seem even able to imagine what the beginning of a belief would be like. They seem to think there is something archaic and antediluvian about those first acts of the mind, by which it opens the open question of the world. It seems a mere mad negation to start from scratch. It seems a barbaric fantasy to begin at the beginning. They no more employ first principles than flint arrows, and regard the first proposition of Euclid as a palaeolithic drawing on a rock. They would almost as soon rebuild all our elaborate and toppling cities of civilisation all over again, from their first foundations, as really dig up one of their own reasons for one of their own opinions.
Easter, which is the spiritual New Year, should be a time for the understanding of new thoughts and the making of new things. The representatives of the rising generation can give us any number of negative reasons for not observing certain forms or traditions. They do not seem to see that it is their business as artists to create forms. They will not realise that it is their business as builders to found traditions. If the old conventions have really come to an end, the others have to do something much more difficult; they have to come to a beginning. I doubt if they have any clear idea about how to come to a beginning. They do not understand that positive creations are founded on positive creeds. To touch but lightly upon the great mystery that is most involved in the idea of Easter, we have seen lately a lively curiosity revolving round the ancient idea of the return of the dead. Perhaps it should rather be called the great and glorious doubt about whether the dead are dead. When that doubt came to trouble a generation of materialists, it naturally turned many of them into spiritualists. The spiritualist is nearly always a converted materialist. He is seldom or never a natural mystic. For most of these men it was enough of a revelation that any light of any sort gleamed through the cracks of the door of death, which they had assumed to be the blank wall at the end of a blind alley. The result on the mass of their sympathisers or semi-sympathisers was something very like what I have suggested as the attitude of the man staring with a blank face at the blue rosette. It is not so much the condition of having discovered something as of being ready for anything. It is not so much that most modern people have found a faith to set against the materialists as simply that they have lost faith in materialism. The sceptic is sure of nothing now, not even of his five senses. It is not so much a new vision as a new void to be filled with visions; and this is no place in which to argue about what the visions shall be.
[GKC ILN Apr 3 1926 CW34:73-74]

Postscript: Speaking as a computer scientist, who is at base a mathematician, it is very pleasant and satisfactory to hear GKC appeal to Euclid in relation to Easter... but you have heard it from me many times before, and this time I shall omit the footnotes and quote from memory: "Whether you are speaking of PIGS or the Binomial Theorem you are STILL talking about God." and also this one: "I never can really feel that there is such a thing as a different subject." GKC is a medieval man; so am I. I think such topics have EVERYTHING to do with Easter, and if God permits, one day I will try to write more about that too.

Christ is Risen! Alleluia!

Good News! Jesus rose from the dead.

Oh yes, I have heard that the original Greek was in the passive, but I rather expect it's a Deponent Verb. (I have no knowledge of such things in Greek; on this some other authority must be consulted.)

However, I will assert - under pain of torture, if need be - that JESUS CHRIST ROSE FROM THE DEAD... and in the most Active sense possible to a mere verb.

Indeed, since all Creation exults on this great day, the day of our human Eucatastrophe, I venture to state that all SUBcreation also exults, which includes such homely things as verbs, and endings, and their mechanical trappings.

Let all grammars and vocabularies bless the Lord!
Let all numbers and equations bless the Lord!
Milo and Humbug and Tock, Azaz and Mathemagician, Rhyme and Reason, bless the Lord!
Let every branch in the Tree of Virtues, let every existing thing in the Kingdom of Wisdom, bless the Lord!
Let all Subcreation bless the Lord! Give glory and eternal praise to Him!

The verb is no longer a merely human thing. God Himself used it: "Et verbum caro factum est." And that's not all! It is silly (and perhaps boringly academic) for someone to explain (with a ponderous grunt) that "the Father 'raised' Jesus" or whatever their explanation is. The Trinity acts as one... we heard all that in Gethsemani, "Not my will but thine be done" - yes, even to the point of accepting death, death on a Cross... as the Father acted, the Word-made-flesh acted, and the Spirit with them likewise.

Yes, Mr. Dickens, we have heard you say something like it before - but we can say it even better: "Christ was dead: to begin with. Or no good can come of the story I am about to tell you." We saw - our eye-witness saw - the Centurion's lance certified the death. He was as dead as a nail-of-crucifixion. "The Cross cannot be defeated, for it is Defeat." [GKC The Ball and the Cross]

And yet... I repeat (in the active voice)

JESUS CHRIST ROSE FROM THE DEAD.

For our God knows the way out of the grave.
[GKC The Everlasting Man CW2:382]

Alleluia, alleluia!

Yes! Run! Quickly! Tell each other this good news! For it really is news. Nobody else has any. [GKC The Everlasting Man CW2:401]

Saying YES and St. Joseph!

Hurray! March 19 - and the "coronation" Mass of Francis I!

I have been busy with many little puzzles and projects, and apologise - but let us keep praying and working - as the old Benedictine motto ora et labora has it - whether we be working at computing or chemistry or fiction or fantasy or cooking or music.

One fascinating project I got to do over the last weekend was to write the code to render a new coat-of-arms I just contrived for my Saga. This is the arms for that secret and ancient organization known as the High Court of Chivalry - I finished it on Sunday but have not yet posted it on the website where it belongs. For the moment, I will merely give the blazon, and you may contemplate what it will look like...

Sable, seme of mullets argent: a cross Or amid four Swords of Chivalry in saltire, points inward; on the cross an escutcheon gules charged with the sun in his splendor Or.

Motto: οὐκ ἦλθεν διακονηθῆναι, ἀλλὰ διακονῆσαι
He did not come to be served, but to serve. Mt20:28

Sword of Chivalry: blade argent, pommell Or, with three gems (Azure,Vert, Gules)

Sorry it doesn't require any sorting, but I did get to do some "sum of angles" computations, which are always fun.

Someday I might try to envision the arms of the Order of Computer Science - should that ever be founded. It probably ought to have this famous curve, the equation for which is

y = x·(1–x)

Oh yes, it's stunning! (Someday I'll get a teeshirt made with it. On the back it can have the equation and below that say "Thank God for George Boole!") And if you don't know why that parabola is important, you had better go and think about it. It's even in the gospel, and this "bit" may well be the motto for our arms:

ἔστω δὲ ὁ λόγος ὑμῶν ναὶ ναί, οὒ οὔ: τὸ δὲ περισσὸν τούτων ἐκ τοῦ πονηροῦ ἐστιν.

Let your word be Yes for Yes, and No for No; whatever goes beyond this, comes of evil. [Mt 5:37]

For today, let us thank St. Joseph the Worker, the Terror of Demons, the Custodian of Virgins, and the Protector of the Universal Church, for his "Yes" to God, and ask him to help us also always say "Yes" to whatever He asks of us.

P.S. Now that I think about it, maybe our arms ought to be like our trees, with the root at the top. Then this parabola could form the curve of the shield. Er... maybe not. But perhaps our crest should be: "A tree inverted, proper."

Sede Vacante

The Apostolic See is now vacant.

Hence, let us BEGIN a Solemn Novena to the Holy Spirit - in supplication for a holy successor to Benedict XVI. And let us continue to pray for the Cardinals, and for the whole Church, until we have a new Supreme Pontiff.

Prayer is the highest of technologies - it is the one single effective communications technique which reaches beyond the physical universe to HE WHO IS, and as you may recall, He told us to pray constantly. We ought to do this, in our homes and offices and labs, for ourselves and our families and our co-workers - and especially when we are confronted by significant cases such as this.

Novena for Benedict XVI

Counting today, February 20, there are 9 days until the Pope's resignation takes effect.

Hence, let us BEGIN a Solemn Novena to the Holy Spirit - in thanksgiving for all his work, and in supplication for him and for his successor.

Prayer is the highest of technologies - it is the one single effective communications technique which reaches beyond the physical universe to HE WHO IS, and as you may recall, He told us to pray constantly. We ought to do this, in our homes and offices and labs, for ourselves and our families and our co-workers - and especially when we are confronted by significant cases such as this.