I just returned home from a two-week visit to Irvine, California, a compact little town about 50 south of Los Angeles. I was visiting friends and family. Before starting the drive from San Jose to Irvine, I queried with MapQuest to check the mileage from my house, Point A, to the destination house, Point B. Although I have made the drive too many times to count and know very well the mileage, I wanted to be sure nothing had changed. After all, the Sun is in a low sunspot cycle and perhaps a small number of sunspots lowered the temperature of the Earth’s core which in turn decreased the Earth’s radius which would clearly change the distance between any two points on the Earth’s surface. MapQuest provided me a fine map and specified the distance between origination Point A and destination Point B to be 380 miles. For proof, see Figure 2. Now I know that MapQuest gives the actual mileage as 380.13 and I just rounded to the nearest 1 mile. If my mathematician cousin (let’s call him Dave) reads this he will call me and make a fuss. But I won’t pay much attention to his gripes. Who could? If you read a previous post “Sock Theory” from June 14, 2009, you would see that “Dave” walks around believing his white socks are most fashionable. I believe his mathematics, but not his gripes. See Figure 1.

Figure 1 Cousin Dave's Fashion

Figure 2 SJ to Irvine

Okay, so I am expecting to drive 380 miles. As I get ready to leave my house, I check my gauges to ensure all is well with my Jeep and the Universe. See Figure 3.

Figure 3 - Odometer reads 000

The gauges show that all is well.
Gas: Full. Good
Battery: Charging. Good
RPMs: Since I am stopped they are 0. Good
Speed: Since I am stopped it is 0. Good
Oil: Got positive pressure. Good
Water temp: Since I just started the Jeep, its low. Good
Universe Condition” Now. Good

Off I go.

I drive nonstop for 220 miles down Interstate 5 to Hwy 58 and make a stop for gas at the Buttonwillow gas station zone. See Figure 4.

Figure 4 - Map of SJ to Buttonwillow

About a mile before the off ramp I check my gauges and something is not quite right. See Figure 5.

Figure 5 - Gauges in Buttonwillow station

My Universe gauge reads above “Now!” Why? What could it mean? I think about it as I cruise to the off ramp, then it comes to me. I have been traveling at 40 mph for 220 miles. When I got on Hwy 5, I thought the speed limit sign said “Maximum Speed 40.” Apparently I misread the sign as the max speed is actually 70. Now I understand why so many cars were blowing by me with occupants waving at me. I didn’t really think I knew that many people. Checking the Universe chapter in the 2009 edition of the Physicists Handbook, I see that if one travels too slow for too long, basic physical laws are twisted, affecting the age of space/time. Geez! I feel lucky to have gotten to the Buttonwillow stations when I did.

Now with a full tank of gas and a clear knowledge of appropriate speeds, I am back on Hwy 5 headed to Irvine through LA.

I arrive at destination house Point B. I pull the Jeep up in front of the house and, as I always do, check my gauges. Everything looks good. I check my mileage, expecting to see 380. But the odometer reads 378. Okay. That’s okay. The difference is negligible and I can account for the 2-mile difference by believing that my odometer is not calibrated exactly with the MapQuest satellite.

Then I realize I am experiencing a surprising event. My odometer reads 378 and the house I am visiting has street number 378! For proof, see Figures 6 and 6.5.

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Figure 6 - Odometer reading in Irvine is 378

Figure 6.5 - House with street number 378

What is the likelihood of that happening? I don’t know, but I liked it and I went to work determining that probability. At first I thought the probability of a match between my odometer reading and the house number would be very small. But maybe it is not. With a good suggestion from my friend and colleague Jim Vilchuck, I thought as follows.

I know by MapQuest and experience that destination Point B is about 50 miles south of LA, making it somewhere between 350 and 400 miles from San Jose. I know my odometer reading will be somewhere in this range. The sample space then consists of the 51 numbers between and including 350 and 400. The probability of randomly selecting one of them is 1/51. So, I could reason that that probability of my odometer number matching the house number is 1/51. So a match should happen about 1 time about 51 visits. The mileage is likely to vary each trip as I make different stops/turns along the way.

But Irvine is closer to 50 miles south of LA than 1 mile south. So maybe the probability of a match is even higher than 1/51. We could say that destination Point B is between 375 and 385 miles. This makes a sample space of 11 numbers and gives a probability of a match of 1/11. That is a surprise result, at least to me.

But now here is an even more surprising event. After being in Irvine for 2 weeks, I make a visit about 14 miles away to a location in Newport Beach. After a nice visit, I leave Newport Beach to drive back to San Jose. See Figure 7.

Figure 7 - Newport Beach to SJ

Seven hours after leaving NB, I arrive home in SJ. I pull into my garage and check my odometer. It reads 377.6. Surprise! See Figure 8.

Figure 8 - Odometer reads 377

Even though I left Southern California from a location different from the Irvine location, the travel distance was still 378 miles. Now it looks likes the number 377 is not the same as the number 378. After all, the last digit of the first number is 7 and the last digit of the second number is 8. But the two numbers are actually the same, 378. Using the well-known Craig Allen Theorem of Equal Numbers, 7 = 8, for large values of 7. Hence, 377 = 378.

Proof:

Now, of course the question is what is the probability that the Jeep travels 378 miles from San Jose to Irvine and matches the house’s street number of 378 and then travels back to SJ from a different starting point and also travels 378 miles? I don’t know. But right now I am going to Jack-in-the-Box to get tacos and a large diet coke. Maybe I’ll work on this problem later.