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Divine Digits
Written March 14, 2008


Little Zoey asked for a dollhouse for her birthday.  "And I know just what kind I want, too," she told her mother.

"Really?  What sort of dollhouse?"

"A big one.  Not too big.  It's gotta fit on the table in my room.  So about this big."  She held her arms apart.  "And the sides will be open, so you can see into the rooms."

Zoey's mother figured that she wouldn't have any trouble finding a dollhouse like that.  But that was before the girl began adding features to her dream home.

"It's gonna have a hunnert rooms, and a hunnert closets, and sixty fireplaces.  And one big chimney on top for Santa."

"My!  Why so many rooms?"

"For all my dollies.  They're gonna live there.  Elmo, and Chatty Cathy, and Betsy Wetsy, and Raggedy Ann . . . ."

"Zoey," her mother interrupted gently, "a tabletop dollhouse is for smaller dolls.  Little plastic ones.  Betsy Wetsy might not fit inside.  She's too big."

"Not too big," Zoey insisted.  "Betsy's just a baby!  But she'll have her own room, just like all the others.  And I'll go in there and take care of her every day."

"You're going to go inside the dollhouse yourself?"

"And I'll climb the stairs and go all the way up to the roof and sit up there.  And the roof will be made of grass.  Blue grass.  And alla windows in the house will be made outa real shiny diamonds.  And in one room I'll have a real live pony.  And every room will have a golden mirror with a fairy godmother inside it, and there'll be a big kitchen with a real oven and a table with high chairs for alla dolls to sit, eleventeen of them, and faucets with all different kinds of juice and hot chocklit.  And every day we'll all go in the living room for a big tea party."

"Sounds like a very fancy house."

"And it's only gonna cost nine dollars.  And nine cents."

Zoey extravagantly added many desirable features to her house.  Now the house is no longer possible, because the features are contradictory.  Small enough to fit on a tabletop, but big enough to contain a girl and her pony?  Luxurious enough to have diamond windows and hot and cold running beverages, but affordable enough to cost only $9.09?

Zoey's mother didn't even try to find what the girl imagined.  She had to settle for something less, because no such dollhouse exists.

But are we sure?  It's impossible to prove a negative.  At least that's what's atheists are told when they assert that there is no God.  They're told that no atheist can prove God doesn't exist.

An example of a negative: "There are no white crows."  You could check every crow you find and confirm that it is black, but that wouldn't constitute proof that there are no white crows anywhere.

So is it really impossible to prove a negative?

Perhaps it is impossible if we use merely anecdotal evidence.  (For example, I've never seen a white crow, so there must not be any.)

But we might be able to prove a negative if we can use logic.  (For example, if the official definition of a crow requires it to be black, a white "crow" is — by definition — not a crow.  It must be some other kind of bird.)

In particular, we can prove at least one negative.  We can prove that Divine Digits do not exist, at least not as I have defined them.

The Divine Digits are two very special numbers I've dreamed up.  I call the smaller one Urim, or U for short, and the larger one Thummim, or T.

Because I was once a physics major, I know a little bit about numbers.  I could spend all day extolling the uniqueness and greatness of these two Digits.  I could inscribe them on plaques, build shrines to them, order my entire life around their sublime relationship.

How shall I describe the Divine Digits?  I cannot count the ways.  Shall I tell you that each is twice as large as the other?  Shall I reveal that adding their square roots together will cure the common cold?  I could claim all sorts of additional attributes.

But it has been revealed to me that they possess, as the most important of their very special properties, the following three Virtues.

First, if you add Thummim and Urim, the sum is 7, the number of days of Creation.

Secondly, if from Thummim you subtract Urim, the difference is 3, the number of the Holy Trinity.

Thirdly, if you multiply Thummim times Urim, the product is 12, the number of the Disciples.

Given these Virtues, we ought to be able to discover the true identity of my Divine Digits by mathematical reasoning.  We only need to venture just a little way into the fearsome world of algebra.  Do we dare?  Let's try.

We begin by adding the first two equations together.  Adding equations together is a common procedure in algebra.  In our case, the result looks like

T + U + T – U = 7 + 3 .

But the positive and negative U's cancel each other out, and 7+3=10.  After making these simplifications, we are left with

T        + T       =   10 .

For this to be true, T must be equal to 5.

We can then substitute that value for T into the equation of the first Virtue.

T + U = 7  becomes 5 + U = 7 .

Or we could do the same for the equation of the second Virtue.

T – U = 3  becomes 5 – U = 3 .

From either equation, it's obvious that U must be equal to 2.

There is nothing wrong with the mathematics.  Using just the equations for the first two Virtues, we have proved that Thummim is 5 and Urim is 2.

However, these numbers do not accord with the third Virtue, which proclaims that multiplying them together should result in a product of 12.  If we multiply 5 times 2, we get only 10, not 12.

Is there another answer?  Perhaps Thummim is 4 and Urim is 3.  That would result in a product of 12 and a sum of 7, but the difference is 1, not 3.

Perhaps Thummim is 5.275 and Urim is 2.275.  That would result in a product of 12 and a difference of 3, but the sum is 7.550, not 7.

Apparently there are several pairs of numbers that possess two of the Virtues but not the third.

If I had claimed only two Virtues for my Divine Digits, I would have remained on solid ground.  But, like Zoey, I went too far, and I bestowed one perfection too many.  Mathematically, there cannot be a pair of numbers with all three of my Virtues!  Therefore the Divine Digits, as I have described them, do not exist.

Many others before me have spoken not of Divine Digits but of a Divine Being.  They have built shrines to this Divine Being.  They have ordered their entire lives around their sublime relationship to the Divine Being.  How do they describe the Divine Being?  They call it "God" and assign many wonderful qualities to "him."

Theologians have been unable to resist claiming limitless perfections for the God that they adore.  They extravagantly add whatever fantastic qualities their inspiration suggests.

For example, they've decided that there can be nothing greater than God.  And they've also decided that God can do anything.  What good would a God be if his powers were limited?

Very well, say the skeptics, is this God able to create another god greater than himself?

If he is able, there can be something greater than God.  If he isn't able, his powers are limited.  Either way, he's less than the ideal God you've imagined.

True believers generally credit God with the following three Virtues.

First, he is all-knowing, or "omniscient."  He knows about everything that happens, particularly as it affects humans.

Second, he is all-powerful, or "omnipotent."  He can do anything he wants to do.

Third, he is all-good and all-loving.  He wants humans to be happy.

But in the real world, bad things happen.  As Tom Flynn puts it, “If the world contains evil, and if God is all-knowing and all-powerful, it has to be his fault!”  And a God who is responsible for evil, though he may be all-knowing and all-powerful, cannot also be all-good.

Bad things can happen only in a world ruled by a lesser God.

Perhaps our lesser God lacks one of the three Virtues.  He may be unaware that there's a problem (not omniscient).  He may be unable to do anything about it (not omnipotent).  Or he may not care (not all-loving).

But a God with all three Virtues could not allow evil to continue.  And because there is evil, this God cannot exist and does not exist.

Of course, we have not proved that no God exists.  We have only disproved one concept of God — namely the idealized Christian God, one to whom we have ascribed more Virtues than are consistent with reality.

We must find a less fanciful description.



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In another story, Zoey speculates about heaven.  Click here.