A.M. Last night Sarah was feeling nervous about labor and had a hard time falling asleep. So I gave her a math problem to solve. The problem was this. A plane on the 45th parallel starts flying west trying to "catch" the setting sun. How fast does it need to go for the sun to stop setting? She solved it for the case of doing it on the equator ( circumference of the earth/24 = 1035.62 mph), but struggled with the 45th parallel location. So I started explaining the solution. To make long story short all you need to do is multiply the equator speed by the cosine of the parallel, so in this case circumference of the earth/24 * cos(45 degrees), or in other words (40000/1.60934) *(sqrt(2)/2)/24 = 732.29 mph, however I started explaining the proof of that, and she fell soundly asleep within two minutes. I felt recovered from the marathon and ran total of 12 today. All of it was with the kids and/or Rob. So Rob ended up doing 4 miles with one of them in 7:36 on hills, Benjamin 7.5, Jenny and Julia 3, Joseph 2, Jacob 1, and William 0.5. Benjamin and I did a 2 mile tempo down the Provo Canyon. The purpose was to assess the damage. For Benjamin, the loss of fitness after the cold. For me, to verify that the cause of 2:44 in Rocket City was indeed humidity and nothing else, and also to measure the recovery from the marathon. We went through the first mile in 5:42, and Benjamin was struggling. So we backed off to a little under 6:00 for the next half mile, and then picked it up in the last 0.5 (5:38 pace) to finish 2 miles in 11:29. It was obvious that Benjamin had suffered significant damage, but on the positive side his fitness was not completely destroyed, and he has made great progress just over the last two weeks. Two weeks ago he struggled at 8:00 pace. Now he can sustain 5:45 over 2 miles. I felt great and the entire time wished I could have felt that way just in the first two miles of the marathon then bring the humidity on. This alone would have made me 40 seconds faster :-) So this run confirmed to me that I am just really really bad at dealing with humidity right now for one reason or another. Maybe it has something to do with that I've had almost zero exposure to humidity over the last 20 years. | 