Thursday, May 14, 2009

milk and honey


Two nights ago, for a Will and Annie bedtime story I read about the twelve spies who went into Canaan. ...ten were bad and two were good... Caleb and Joshua were the fearless minority who considered it worth the risk. They were excited to see what God had for his people.

I can remember reading this before and thinking of Caleb and Joshua as faithful, adventurous, courageous, obedient and righteous in their attitude toward the task. The others always seemed like wet blankets. Cowards.

This time when I read it, I seemed to hear ten reasonable voices concerned about the feasibility of a plan, the numbers and dimensions of the enemies, and the strength of the strongholds. Joshua and Caleb seemed like goofy little kids saying, "Yeah, but look at the size of these grapes! Moses can we go, can we can we can we, PLEEEEEEEEEEEASE!?" And it sounded reasonable to think about not going. And it sounded ridiculous to risk your neck for a taste of milk and honey. And I realized that I have become a coward.

Numbers 13:27 They gave Moses this account: "We went into the land to which you sent us, and it does flow with milk and honey! Here is its fruit. 28 But the people who live there are powerful, and the cities are fortified and very large. We even saw descendants of Anak there.
...
30 Then Caleb silenced the people before Moses and said, "We should go up and take possession of the land, for we can certainly do it."31But the men who had gone up with him said, "We can't attack those people; they are stronger than we are."32And they spread among the Israelites a bad report about the land they had explored. They said, "The land we explored devours those living in it. All the people we saw there are of great size."

They saw the same things, and there is nothing to indicate that they differed on their assessment of the problem, only on their assessment of the risk. Caleb and Joshua had seen the soldiers and the terrain and the fortifications. But they also saw God's promise as a tangible security, and they breathed richly of the blessings of his plans. I suspect that for Joshua and Caleb, the time in Canaan was an amazing experience, a vibrant and overwhelming exposure to God's provisions for his people, an invigorating and reassuring security. Their comrades on the same trip slept in the same hills, walked on the same paths, crossed the same rivers, ate the same fruit and paced the same valleys to survive a terrifying foray into enemy land. No, they didn't see different things. Joshua and Caleb simply knew the value of milk and honey.

God, please grant me courage to pursue your blessings.

Tuesday, May 5, 2009

solution: streets and avenues


There are 729 ways to travel from the corner of 3rd Ave & 12th St to the corner of 8th Ave and 5th St. In the problem statement, I did not specify that north or west made the numbers go up or down. Correct diagrams could therefore differ, but I did not want to distract from the main riddle, that you must travel five blocks in one direction and seven blocks in the perpendicular direction.

Any valid shortest distance by road will need to be 12 blocks total, five of those being one direction and seven being in the other direction. In my diagram, I need to go east and north. As long as I go five blocks east, seven blocks north, zero blocks west and zero blocks south, I will arrive at the specified location. I can mix up the order...

In other words, I need to travel 12 blocks and 5 of them need to be east (the rest north). Which ones should be east? The answer is a combination, 12C5 = 12!/(5!*7!) = 729 .

solution: burning tent

In the burning tent problem, we have a starting point (the camper at the moment of realization) and a finishing point (the burning tent). We want to minimize the distance from the camper to the tent via the river. A first step may be to realize that this task is not the same as minimizing the first leg or the second leg of the trip. That is, going straight to the river does not give us the shortest route, and neither does going to the point of the river closest to the tent. The answer will involve a happy medium. As such, calculus is an option.

The clever way to solve this problem is to imagine that the point along the river bank has been chosen and we are watching the reflection of the camper across the line that is the river bank. The camper and his reflection will always be the same distance from the river. In other words, if we choose a target point on the river that gives the camper the shortest distance, it also gives his reflection the shortest route. Therefore, choose the point that is on the line between the camper's reflection and the burning tent. The shortest distance is given in the comments of the question.