Prayer and Wonder - or, the Mistake about the Computer

I had a fascinating and wonderful experience last weekend - I threw my star charts into my vehicle and went to visit some dear friends in a distant star system... Ahem, I guess I ought not go into details about who they are or how I got there. But they are Chestertonians, and there are one or two experiences I wish to tell you about.

First, their church was having a festival that weekend and to my delight they had a used book table! I found a small book by Father Hardon called The Theology of Prayer which I grabbed - a glance told me it was a critical reagent in my current experiment of developing a new text on the technology of prayer... and - even better - once I started reading it, I learned that it contained the answer to an issue we Chestertonians are concerned with! Oh yes. In fact, it ties into... no, no. It forms the true basis for the larger issues, such as government, economics, and education, and the Great Evil of the age - the hatred of life - which Chesterton called "Eugenics" and which goes by other names in our time.

But in order to set the stage for this discussion, I must tell you about another matter. I donned my doctoral robe for a brief time on Sunday evening and gave a miniature lecture to a bright young man of 14. Earlier that weekend I had been speaking with his father on the "Magic Box" of our modern days, and how all who touch it become endowed with supreme intelligence and wisdom, regardless of their knowledge of automata theory, the XOR, the mutex, recursion, floating-point, ASCII and all the magical tools within that Magic Box. We laughed as I said it is as silly to credit a 7 year old child with "knowledge" of the Computer because he plays with it for an hour in the classroom as it is to credit him with "knowledge" of the Internal Combustion Engine because he rides in a big yellow bus containing one for an hour on his way to and from that classroom! Oh yes.

So, just for fun, I decided to ask my young friend whether his father had shown him the really stupid math mistakes a computer can make.

He stared at me - as if I had asked him about the edibility of rocks.

Oh, yes, I told him, I know a very simple math problem that I knew he could perform (since he was 14) but was beyond the ability of the computer to handle. Again he stared, as if I had said that most pigs are seen in floating the air.

So I told him I would show him. It is something, I said, as easy as doubling a number. Of course he already knew one plus one is two, two plus two is four... and I proceeded to rattle off the powers of two up to the 20th power (since I use many of them at work, I have them ready to hand - nothing surprising there). I scribbled this series down on a scrap of paper and he nodded.

1
2
4
8
16
32
64
128
256
512
1024
2048
4096
8192
16384
32768
65536
131072
262144
524288
1048576

All that was obvious to him. So I asked him, if I had you do this doubling another dozen times, on paper, would you have any problem? Of course he smiled and shook his head. But I think he was starting to wonder what this was leading to, and began to feel uneasy.

So, I smiled and asked, will the series of doublings ever get smaller?

HUH??? he asked. Smaller? How can that happen?

Oh, I pointed to the computer. Let's just ask the computer to try this very easy little homework project, shall we? So I typed in a very tiny program, which began with one and repeatedly doubled it, counting 20 loops. It produced the exact list of numbers I had already scrawled on paper and listed for you above.

He shrugged, and I smirked. Now, let's just have the computer repeat until the doubled number becomes SMALLER. I typed in what must look like the silliest program ever phrased to a computer - completely sound, and accurate and valid, but something never usually conceived of by most programmers. Rather than show you the actual code, I want you to imagine writing these instructions to someone:

Start with one, and keep doubling it until the new number becomes smaller than the previous number.

Very nice. Then, I said, once the doubled number has become smaller, print "I am finished" and stop.

What? Oh, all right, I will show you the code...
#include "stdio.h"
main()
{
int i,j,k;

i=1;
k=0;
do

{
j=i;
i=j+j;
printf("Loop %d: %d doubled is %d\n",k,j,i);
k=k+1;
}

while(i>j);

printf("All done.\n");
}

I pointed to the screen, and asked my young friend: So, will the computer ever stop?

But he is smart and did not say "NO" - instead he shrugged. So I said, let's see what the computer will do - and I ran the program - and this came out:

Loop 0: 1 doubled is 2
Loop 1: 2 doubled is 4
Loop 2: 4 doubled is 8
Loop 3: 8 doubled is 16
Loop 4: 16 doubled is 32
Loop 5: 32 doubled is 64
Loop 6: 64 doubled is 128
Loop 7: 128 doubled is 256
Loop 8: 256 doubled is 512
Loop 9: 512 doubled is 1024
Loop 10: 1024 doubled is 2048
Loop 11: 2048 doubled is 4096
Loop 12: 4096 doubled is 8192
Loop 13: 8192 doubled is 16384
Loop 14: 16384 doubled is 32768
Loop 15: 32768 doubled is 65536
Loop 16: 65536 doubled is 131072
Loop 17: 131072 doubled is 262144
Loop 18: 262144 doubled is 524288
Loop 19: 524288 doubled is 1048576
Loop 20: 1048576 doubled is 2097152
Loop 21: 2097152 doubled is 4194304
Loop 22: 4194304 doubled is 8388608
Loop 23: 8388608 doubled is 16777216
Loop 24: 16777216 doubled is 33554432
Loop 25: 33554432 doubled is 67108864
Loop 26: 67108864 doubled is 134217728
Loop 27: 134217728 doubled is 268435456
Loop 28: 268435456 doubled is 536870912
Loop 29: 536870912 doubled is 1073741824
Loop 30: 1073741824 doubled is -2147483648
All done.

Of course it stopped after the 30th repeat - as I expected - and he started laughing. (So did I - I have a very low humour threshold, as you may know by now.)

When I had control again, I told him: Now you have seen a computer perform a very trivial, elementary arithmetic problem and get a completely WRONG answer. And he smiled and nodded. But I said, let us be clear about what is going on here. I then set up another very similar program which started with one and continually added one to the previous value, until the total got smaller. However, I ordered the computer to print the LAST number before the decrease.

Before I ran the program I asked my young friend how fast he could count: Could you count to two billion I asked. Again he stared, wondering how long that would take. (In case you are wondering too, at one number a second, it would take over 63 years.) So, I said, you know you are good at counting, but you are slow. Let's see how the computer handles this new problem... and I started it running.

In a very short time (under a minute) the computer printed 2147483647, which was the last number it had counted to - yes, by ones - before it added wrong and got something smaller.

He laughed again. Then I said: Now you have seen, very briefly, the correct view of the computer. It is faster than we are, but it is still making a mistake, for we, unlike it, know that numbers do not decrease when we add one to them! We must always know and understand the tools we use, and their particular limitations - for the computer is NOT magic! Just as a car is not legs, a computer is not brains: it does not "add", it does not "think" - though it can do wonderful things, if we are careful about using it. (If you want to know MORE about this and why, see me after class. Hee hee!)

Now, what does this lengthy narrative have to do with prayer - and with Chesterton?

Simply this: the first and foremost act of worship of God, what the theologians call "adoration" is simply wonder at God - at Him as He is, at His creation, at His inspirations by which we poor fallen men make bridges and software and cakes and poems and rock songs, at His work to enter our human family and make Himself part of our world. We need to admire Him for what He is, which we know through what He does, directly or indirectly. (cf. Eucharistic Prayer IV: "All Your actions show Your wisdom and love.") We need the true view, since "the object of my school is to show how many extraordinary things even a lazy and ordinary man may see if he can spur himself to the single activity of seeing." [GKC Tremendous Trifles 6]

Which is why I did what I did: in two tiny programs I gave my young friend a miniature lesson in the true view of computers, and he could wonder - he could admire them for what they are.

I can now answer the question our esteemed blogg-mistress posed some weeks back about wonder and why the modern world seems to have lost its sense of wonder. There is a theological reason for it. People sense that wonder arises from the surprising power and goodness and delight of God, in Himself and in His works - and they do NOT want to be reminded that He is responsible.

This is why there are lots of people who do not like Chesterton. They do not want to be reminded of God, of His work in Creation (cf. any of Jaki's works) or of His work in sub-creation (cf. Tolkien, Sayers and GKC) or of His work in what we call "Salvation History". But for me, and some friends such as I visited recently, Chesterton and creation and computing - and pedagogy (what and how we teach) - and the Church and wonder and prayer are all inter-related. Hence, in order to renew the sense of wonder in our world, we must begin with God. And you will find as you proceed that you will include addition and computers and fantasy stories and poems and rock music and cakes and all kinds of things: "But seek ye first the kingdom of God and his justice: and all these things shall be added unto you." [Luke 12:31]

No wonder GKC wrote "I never can really feel that there is such a thing as a different subject." We can entertain ourselves with our studies of philosophy and literature, our tech and television and sports and drink-and-drugs, and "fruitless adult activities", but they are only distractions to keep us from facing Reality. (See GKC on this in his book on Aquinas.) There really isn't any such thing as a "different subject" - all things are God's and point to Him, and to see them all we need to do is open our eyes:

The axe falls on the wood in thuds, "God, God."
The cry of the rook, "God," answers it
The crack of the fire on the hearth, the voice of the brook, say the same name;
All things, dog, cat, fiddle, baby,
Wind, breaker, sea, thunderclap
Repeat in a thousand languages -
God.
[GKC "the Notebook" quoted by Maisie Ward in Gilbert Keith Chesterton 64]

Or, as was written almost three millennia ago:

The heavens shew forth the glory of God, and the firmament declareth the work of his hands.
[Ps 18:2]