To Better Know God: A Mathematician's Quest

By R L McCasland

Perhaps everyone who has ever considered the existence and the nature of God has struggled with various questions of faith. The author takes a contemplative look at certain questions commonly regarded, and some questions which maybe are not so common, and presents well-thought-out answers to each. These answers, while having been formulated in the cool precision and logic of the mathematical thought process, are supported by references from Scripture, and by experiences in the author's past, including sermons preached by some of the finest ministers the church has to offer, both in Texas and in Scotland. The reader should find plenty of food for thought.

• Language: English
• Publisher: iUniverse
• Release date: Aug 8, 2000
• ISBN: 9781469733623

R L McCasland

Dr. Roy McCasland has taught Mathematics at three universities in Texas, with several extended visits to the University of Glasgow in Scotland, and published numerous original research articles. He is a lifelong Methodist, having served his home church in Fort Worth, Texas, in many capacities, including Lay Leader.

Book preview

1

A God Infinite in Wisdom,

Power and Love

So how much is ‘infinite’, anyway? Does it matter? Not that this word is by any means the most important of the five key words in the title of this chapter, though it probably is the least talked about.

If we are prepared to believe in a god of any sort, then we should definitely believe in an infinite one. A finite god is of course no god at all. And if we accept that God is infinite, then it would surely do Him an injustice for us to merely spend a fleeting moment contemplating that infinity. Indeed, perhaps most of us, when confronted with the concept, simply shrug and say to ourselves something like, Well, I know that infinity is much bigger than anything I can handle, and go on about our other business. We really should muster a bit more effort than this, in order to come to terms with the Majesty before us.

For without this effort, we are all likely to be guilty from time to time of trying to put limits on God. We will tend to think that he responds to given situations in much the same way that we would. We will occasionally see Him as being in our own image, rather than the other way round.

Let us endeavor to stretch our minds a bit, with a view towards gaining a fuller and more precise understanding as to the nature of

God. Now some will say that this exercise is of no value at all, since in the end, no matter how long or how hard we try, we still will not be able to really comprehend infinity. However, our Lord tells us to be perfect, as our Father in heaven is perfect. And though we all know beforehand that this is an impossible goal for us to truly reach, we understand that there is merit to whatever effort we make to this end. So too, perhaps, will our current exercise prove.

Now, to begin our task. Let us first realize that we are in a sense speaking of a measurement of some sort. And rather than try to measure a Being, let us focus on one aspect, say for instance, how much Love God has for us. And in order to measure any quantity, one needs some unit of measurement by which to compare. The difficulty of course is that in this world there is no physical object which is in any way infinite, not that anyone has personally encountered, in any event.

So we turn to the world of mathematics. To start, we need nothing more (nor less) sophisticated than our counting numbers, 1,2,3, and so on. We can all agree that there are infinitely many of these, for the simple reason that once you think you’ve found the last one, you can easily spot another. Now pretend that you have managed to stuff all these numbers into one bag. Of course, the bag itself would have to be bigger than any bag you’ve ever seen, but give it your best effort.

You are now perhaps tempted to say, Hold on. You have just asked us to imagine an infinite bag, the sole purpose of which is to help us grasp the concept of the infinite nature of God’s Love. But this is not the end of our exercise. Even if your imagined bag is finite, that will do quite nicely. Only pretend that it is infinite. But do not think that I’m going to suggest that this bag in any way can measure that Love.

Mathematicians have proven that there are actually different ‘sizes’ of infinity, and thus far in our exercise we have simply considered only the smallest of these infinities. Indeed, from a branch of mathematics called Measure Theory, we learn that these counting numbers are just a small part of a much larger set of numbers, the real numbers (for those who happen to be interested). In fact we can actually ‘measure’ the relative sizes of these sets, in much the same way one can relate the sizes of a centimeter and a meter. And what we find is that, though we have infinitely many counting numbers, they collectively measure zero, compared to the real numbers. In other words, a bag containing the larger set would so dwarf the smaller bag as to effectively render the latter invisible. And yet, both bags are infinite.

But does it end here? Of course not. There is another collection of numbers, which indeed contain our set of real numbers (which still contains our set of infinitely many counting numbers). And yes, the real number bag measures zero relative to this new bag, albeit with an obviously necessary adjustment of our measurement scale.

In fact, what we have is an infinite sequence that looks like this. First, we have the infinite bag of counting numbers, and sitting next to it is our real numbers bag. Now in order to see the entire real numbers bag, you have to back so far away that the first bag becomes invisible. But there is a third bag, which is likewise so massive, that in order to see it in its entirety, you have to back still farther away, until the second bag is no longer visible. And there is yet a fourth bag, and a fifth bag, and on and on, continuing indefinitely.

And God’s Love cannot be contained in the whole lot of them.

* * *

Now what are we to make of all this? How are we to respond? One immediate response should be complete and utter humility. Since God encompasses all that we have just imagined, and more, surely each of us by all rights should be as no more to Him than one of our original numbers. Why should God, in His infinite-ness, be mindful of all of humanity, let alone any one of us individually? And yet Jesus, who certainly knows, tells us that He is not only mindful, but that He loves us everyone, individually. Indeed, we are told that not even a sparrow falls to the ground without our Heavenly Father knowing it.

And there is something else (with God, there is always something else). The next time you get the feeling that you have simply run out of love, or patience, or mercy, or forgiveness, or whatever we have in Christ, you know where a literally inexhaustible supply exists. And you know that there is so unimaginably much of whatever you need, that God will certainly be willing to share. All you need to do is ask.

Now an even greater wonder is this: How is it that the Son of God could keep his infinite nature intact, even when He humbled Himself and became one of us, and lived and walked among us?

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How We Begin to Know God

How is it that an individual can look at some markings on a page, and immediately conjure up a mental image, associated with those markings, and that is roughly equivalent