Odds & Ends #2

Soon after I began this blog, I grouped several small comments into one post I called Odds & Ends, and said I would probably do so again as the occasion might warrant. In that first Odds & Ends, I commented on several blog-related items, such as the Bible version I was using, where my blog’s heading picture came from, etc. Today, I offer a second such collection, but do so in the famous words of Monty Python’s Flying Circus, “And now for something completely different. . .”

There are a few things that have been on my mind that are not directly related to matters of faith or theology (or so it may seem!), but which I want to “get off my chest” as it were. Not knowing where else to go with these thoughts, I decided to post them here. You may read, ignore, or reply as you wish!

Earthrise: The first thought has to do with the famous photo taken on Christmas Eve, 1968 by Apollo 8 as it orbited the moon, showing the earth in the lunar sky just above the horizon. The photo is called, “Earthrise,” and it is not only a beautiful picture, it is also a powerful reminder that all of us share this one planet together; that in the vastness of space, this one “blue marble” is where physical life exists. The implication is that we need to take care of it and each other – not a bad idea – and good theology as well! (Genesis 1:26-30, 2:15 and Romans 15:1-2 among many other verses).

Last year, a Japanese video lab released an enhanced video showing the earth actually rising in the lunar sky, lifting above the horizon until it is full-orbed in view. The description read with it placed the camera’s location at the moon’s south pole. The announcers who showed it on their national news program were suitably awed and impressed by the video.

The only problem is that from the moon’s perspective, there never has been an “earthrise” because the same side of the moon always faces the earth! The only way to watch the earth “rise” in the moon’s sky is to do what Apollo 8 and various moon probes did, and that is to fly over the surface toward the side of the moon which faces the earth. As you approach the earth-facing side, the earth would appear to rise due to your motion. But, if you took a still photo or video of the earth from anywhere on the moon’s surface, the position of the earth in your sky would never change. You could stand there for hours or days or weeks or centuries, and the position of the earth in your sky would be the same. You could see the earth rotate and watch as first the Americas and then the other continents passed in and out of view, but the position of the earth’s globe would always be in the same place, relative to where you are standing.

Why is that? Technically it’s because the period of the moon’s rotation (one 29.5-day month) is the same as the period of the moon’s revolution around the earth. The result is more familiar to us: the same side of the moon always faces the earth; whether the moon is full or a crescent or dark, the same side faces us all the time. It always has; not until probes photographed the back side of the moon did we have any idea what it looked like. Now both sides have been mapped, but just as we will never look up and see the far side of the moon, the far side of the moon will never see the earth; hence, no earthrise . . .

Oh, and by the way, even if the moon rotated faster so that both sides of the moon got to see the earth, a camera at the moon’s south pole would not see an earthrise; it would see the earth circle in the sky like the sun circles our sky above the arctic circle in the summer. Seeing an earthrise from the poles would be like the sun coming up in the north and setting in the south here on the earth. So. . . “earthrise” makes a great still photo, but no video from the moon’s surface.

So where does theology come in? Check out scriptural references to God’s creation of the moon. (Genesis 1:16 – creation; Psalm 89:37 – as a witness to God’s faithfulness; and Psalm 104:19 – to mark the seasons.)

The Monty Hall Problem: No, I’m not saying Monty Hall has or had a personal problem of some kind! What I’m referring to is a math problem based on the game show, Let’s Make a Deal, which was produced and emceed for many years by Mr. Hall. The problem has to do with the choice faced by a contestant when confronted by three doors, behind one of which is hidden the grand prize. The contestant must choose one of the three (let’s call it door A), which remains closed and unrevealed. Then Mr. Hall opens a door which does not have the grand prize (let’s call it door C), and asks the contestant whether he or she wants to keep the door already selected (door A), or trade it for the other unopened door (door B).

The contestant knows that the grand prize is behind either door A or door B; the problem is, should the contestant hold on to A or switch to B? Which choice is more likely to win the grand prize? Or are the odds the same for either choice?

Mathematics offers a solution to the dilemma. According to several proofs, including one presented in episode 13 of the TV show, Numb3rs (yes, that’s how it’s spelled) and in the movie 21, the contestant will have a better chance to win if he or she makes the trade for door B. The math says that the odds of winning by switching almost double the odds in your favor.

Huh? Aren’t the odds equal? You have two choices, A or B. Basic math probability gives the odds of either choice as 1/2 or 50%. Two choices, one desirable outcome = equal odds. How can mathematicians contradict that simple formula?

Their answer is that when you first chose door A, the odds of it being right were 1/3 (I agree), so the odds of B or C being right was 2/3. Because door C was a losing door, the odds of door B being the right choice remains 2/3. So, door B’s odds are 2/3, door A’s are 1/3, so you should switch to double your odds of winning. So the theory goes, and proofs of it are readily available on YouTube.

I am at risk dabbling in what is not my field of expertise (if I have one), but even after seeing the math proofs, I would still insist it makes no difference which door you chose, for the following two reasons: 1. First, it doesn’t matter how many choices were first available which narrowed it down to just two doors. There could have been 25 choices like on Deal or No Deal? When you get down to the final two doors, there are still just two choices. What went before doesn’t matter and doesn’t affect that choice.  It’s like tossing a coin: even if you toss 25 heads in a row, the odds on the next toss are still only 50% heads and 50% tails (assuming it’s not a 2-headed coin, which you might begin to suspect at that point!). Now, if you tried to predict at the beginning that you would toss 25 heads in a row, that would be different – 1/2 to the 25th power or 1/33554432. But on the 26th toss, the odds for that toss are still 1/2 for heads and 1/2 for tails.

2. The second reason I question the advice to switch doors is because the “proof” which is used to suggest the change is flawed. It switches the basis on which the two odds are calculated. Door A is rated using a base of three doors, but door B is rated based on adding two doors together. Of course the odds will be different if you set it up that way. Each door (A, B, and C) had only a 1/3 chance of being the prize door at the beginning, but when door C was eliminated, those initial odds vanish, and in the final selection doors A and B each have a 1/2 chance to hold the prize. Q.E.D. as they say in math proofs (Quod erat demonstratum = Latin for “what was to be demonstrated” or “thus proven” or more rudely, “take that!”).

What is the theological reason for this math question? I came across it while researching logical and ethical dilemmas for the course I taught on Christian ethics at St. Peter’s. It has been bugging me ever since . . . Also I would say not to bet your life or eternity on chance or the questionable odds of choosing which religion/door has the true prize behind it. There is only one door to eternal life, and that was the one promised by Jesus Christ, who said in John 10:9, “I am the door. If anyone enters by me, he will be saved and will go in and out and find pasture.”

May the Lord bless you and keep you, the Lord make his face to shine upon you and be gracious to you, the Lord look upon you with favor, and give you peace. Amen.

Read: Genesis 1 and John 10