Tuesday, October 04, 2005

The Nature of Pizza (Or, I'm a Geek)

So here's my musing for the last few days: Suppose I have a coupon for a free pizza. Which of the following coupons is the gospel more like:
Good for one free large pizza, up to four items. Pick-up at any participating pizzeria. Available at all participating stores. Coupon must be presented at time of purchase. Coupon may not be used with any other offer.
or
Good for one free large pizza, up to four items. Call 1-800-PIZZA4U and request your free pizza. Delivery only. Coupon must be presented at time of delivery. Coupon may not be used with any other offer.
With the first coupon, it's pretty flexible to get your pizza. Drive around a while and one is sure to spot a Pizza Hut, a Hungry Howie's, or even a Little Caesers. As long as one drives in the right area (a city) and can spot signs, one will end up with a free pizza.

With the second coupon, a certain level of precision is required. Phone numbers are not self-correcting. 1-100-PIZZA4U will not reach the free pizza hotline. It's not enough to merely be 'close' when one dials the number. There are parts of the 2nd coupon that must be gotten exactly right.

So which is the gospel more like? Is the gospel a matter of ballpark? If you are in the right area with reasonable beliefs, you are welcomed into heaven? Or does it require a precision in certain ways in order for the pearly gates to be opened? (Note that both coupons have a lot of flexibility - language spoken, pizza toppings, time of day, etc. The second coupon is still flexible - just not in every way.)

(And for the bonus questions: Is the gospel more like pick-up or delivery? Why?)

For the engineers and mathematicians, the question is this: (The rest of you can tune out now.)
Let x=0 be a line representing perfectly accurate theology.
Let (0,0) be the core aspects of the gospel.
Let y=mx+b represent a line corresponding to our beliefs.
(conveniently, you can't choose an m and b such that x=0 for all y, as we assume no one has perfect theology.)
What are m, b such that one is accepted into heaven?
For the non-math majors, m determines the slope of the line. By picking a larger m, the slope becomes steeper (and closer to matching our x=0 line), representing beliefs closer to the truth. By picking a smaller m, our line becomes flatter (m=0 is a flat line) representing beliefs that are the furthest from the truth.

b represents the intercept point of the line with the y axis (x=0). As b increases, the line moves up on the graph and away from (0,0). As b decreases, the line moves down the axis.

3 comments:

Anonymous said...

Hm, I don't know about this line analogy, Al. Okay, I know you want to let b = 0. We'll allow that. The equation then becomes: y = mx. Since you're letting x = 0 represent the line of "true theology," this means that the x* value on our y = mx line gives us the distance between our belief on topic y* and the "true" belief on topic y*.

Solving for x, we rerepresent the line as x = y/m. We see that no matter what value we choose for m (small or large), as y approaches infinity, so does x. (Note: this result holds independent of the b value).

Basically this boils down to this: for any given person who has the line y = mx, they will necessarily have the core aspects of the gospel and yet will approach being infinitely wrong on other topics. I think that we can be infinitely wrong on some topics (ones with a strict yes-no answer), but the implication still bothers me.

This result also means this: if person i has a small m value and person j has a large m value, the "approaching being infinitely wrong" result holds for both. The only difference is that person i will approach being "infinitely wrong" at a faster rate than will person j. And what might rate have to do with anything?

Perhaps you want to use a tangent function instead of a line, so that you can still vary the distance from the origin (0,0) but so that you can put some bounds on how far people can be allowed to drift from "true" theology?

P.S. The other implication about using the line y = mx is that the distance from the line x = 0 is the same whether or not you use m or -m. This means that you and a friend are "equally wrong" if true theology says that the answer is 0 but you say that it is 2 and your friend says it is -2. I'm not sure that issues are always that symmetric.

P.P.S. I'm annoyed that I can't use subscripts in blogger. :)

P.P.P.S. I apologize to everyone for my nerdiness.

Yi said...

Haha, you guys crack me up, Haha :) Alan, you sure like pizza a lot, don't you?

Lindsey said...

Katie, that is the most awesome reply to a post that I have ever read! :-)