Saturday, September 19, 2009

In the numbers

But maybe not the way you were thinking

The September 2009 issue of Acts & Facts from the Institute for Creation Research contains the usual collection of strained creationist arguments. It also, however, carried a testimonial from a grateful mother who has been “educated” by ICR's publication:
Thank you for sending me Acts & Facts over the years. I have gleaned much from the articles. Even though I am not a scientist, I have been able to write arguments to my son, who was persuaded to accept evolution in college. I’m sharing those with you, so you can see how your ministry has touched my life personally.
There follow some excerpts from one of the woman's ICR-inspired messages to her college-educated son. She had hit on the scheme of belaboring him with the old “design” argument:
Every design carries in it the signature of its creator. So, normally, one viewing a creation, and who is trained, can recognize that signature. It can be recognized because it tells the observer who made it by displaying certain characteristics that the creator endows it with and that reflect the character of the creator.

But I read on and discovered an argument that caught my attention. Clever, clever creationist mom! It turns out that Sudoku proclaims the handiwork of the creator!
I recently discovered Sudoku puzzles. Each row, column, and square of nine squares has to have the numbers 1 to 9 in them and the numbers may not be repeated in any row, column, or square of nine squares. The outcome, however, always results in a design of numbers, unique from any other puzzle except one that duplicates itself. In order to solve a puzzle, you must figure out an intelligent strategy to end up with a “unique design” in the end.

Unique design is the operative phrase. It takes intelligence to create this design. If you just randomly stick in numbers you will never come to the organized end result. Solving these puzzles helps prove to me that evolution is a lie. Randomness for the most part results in chaos. Each Sudoku puzzle may only be solved by thoughtful manipulation of the numbers until a unique pattern (design) is formed.
Our anonymous creation mom is not responsible for the emphasis in the sentence about chaos. I added that. The phrase “for the most part” drew my attention. Did she notice that she just left the barn door open?

No one argues that random variation usually results in order (or increased fitness in a species). I mean, unless you are an ignorant creationist setting up a straw man.

Creation Mom is also hung up on the word “unique.” Here again she is missing something important, just as most creationists do. Evolution is not goal-driven. There is no target. There can be many variations that lead to increased fitness. Natural selection is not driving any species toward a foreordained conclusion. (Creationists who think evolutionists claim this are often misled by experiments such as the much-discussed WEASEL program by Dawkins.) The Sudoku puzzle is therefore a terrible choice for an anti-evolution argument. Valid Sudoku puzzles are anything but unique. Even if a particular instance of a puzzle has but one valid solution, valid Sudoku patterns are anything but rare.

In 2005, Bertram Felgenhauer of Dresden and Frazer Jarvis of Sheffield demonstrated that there are 6,670,903,752,021,072,936,960 valid ways to fill in the 9 × 9 Sudoku grid.

We're not going to run out of Sudoku puzzles any time soon.

Of course, valid Sudoku grids are rare in a relative sense. There are, after all, 9! ways (362,880) to fill a 3 × 3 grid with the integers from 1 through 9. Since there are 9 such grids in a Sudoku, there are (9!)9 ≈ 1.09 × 1050 candidates for Sudoku puzzles. That is, there are many, many more invalid grids than valid ones. But randomly generated grids containing the integers 1 through 9 in each of the 3 × 3 subgrids could be easily checked for validity—just determine whether each row sum and column sum is equal to 45.

That's an extremely simple criterion for determining “fitness.” (Cue the infinite number of chimps—or weasels.)

Creation Mom elaborates her argument with some cant about “random organization,” which she knows won't turn monkeys into humans.
There is something of the order of 2 percent difference in the genetic make-up of man versus monkey. That’s according to what scientists now know, but if you were to replace the 2 percent monkey with the 2 percent that is man, you will no longer have the pattern of a monkey, but a man. The pattern for a monkey doesn’t randomly organize (an intellectual activity) itself into a more complex system. To create a more complex system, you need to engineer (again an intellectual activity) the lower step to the higher by intelligent manipulation. It will not happen through random processes any more than you will be able to create a specific Sudoku pattern through anything but intelligent strategy.
Sorry, Creation Mom. A simple algorithm suffices to separate the Sudoku wheat from the chaff. Natural selection suffices to separate the useful variations from deleterious ones. God as Sudoku master is no more persuasive than God as watchmaker.

But I'm sure the watchmaker was already enough for you. Was it enough for your son, too? (I noticed you didn't say.)


Joshua said...

I think there are two other things going on here:

First, Sudoku involves numbers rather than words. So people perceive it as requiring more intelligence.

Second, the ID people have made it a fad in creationist circles to care about arguments that look mathy. This letter fits that general trend.

The Ridger, FCD said...

I've see Sudoku done with letters and with symbols...

But yeah: it looks like math.

Joffan said...

On checking Suduko grids...

After filling each subgrid with digits 1 to 9, row and column totals are not enough to guarantee validity of the whole gird. Of course the necessary checks are still fairly simple.

Interestingly there are (only) two ways to partition the numbers 1 to 9 into three sets of three such that each set totals 15, which this grid illustrates:

6 7 2
1 5 9
8 3 4

(read across and down). Now each 3x3 block of a Suduko grid can be filled with some variant of this (rotated, transposed, row-shuffled etc), and all rows and columns will always total 45 without any guarantee that the grid is valid (ie. that each row and column consists of exactly the digits 1 to 9 also). Of course there are also many other ways to have valid subgrids and totals without having a valid full grid.

No doubt interesting and efficient algorithms exist that can generate valid Suduko grids.