912 Odd Musings

Wednesday, October 4, 2006

Today I delivered a handful of Pilot's Logs to a marina about 9 miles south of the Bear Mountain bridge. Five and a half hours, a little over 150 miles. It was a beautiful day for the drive (although it would have been much nicer to be out of the car), sunny and high 70s. Route 9W along the section just above and below Bear Mountain is very scenic. I pulled into overlooks several times on the way home, including one that overlooks West Point.

I got into an odd train of thought on the Throughway on the way south, concerning infinity. (I've never heard this argument before, so there must be something wrong with it....)
No even numbers (except 2) are prime,
all prime numbers are odd,
odd numbers can therefore be grouped as prime or not prime,
and all non-prime odd numbers are the product of odd numbers.

So all numbers greater than 2 are

• Even, factors are even x even;
• Even, factors are even x odd;
• Odd, factors are odd x odd; or
• Odd and prime

When you start grouping together all unique combinations of multipliers, 1/4 of the sets are even/even, 2/4 are even/odd, and 1/4 are odd/odd.

• Therefore there are three times as many even products as there are odd non-prime products.
• Since there are as many odd numbers as even, and only 1/3 of odd numbers are non-prime products, then two thirds of all odd numbers must be prime.
• Therefore the average difference between prime numbers should be less than 4.
• But if you look at a list of the first 1,000 prime numbers, the 1000th prime number is 7919.
• That's an average difference of almost 8.
• There are 105,097,565 prime numbers between 2 and 2,147,483,647 (ref. here).
• That's an average difference of about 20.
• It's reasonable to assume that the difference increases as the numbers go up (primes get more scarce because non-prime multipliers get more common).
• Therefore, there's a huge (impossible) clump of prime numbers up there somewhere taking up the slack,
• or there's a fallacy in the argument - can you spot it?
  

Or, third possibility, there's something holding the end of the chain, and it's overwhelmingly prime, and very very odd.

792 Friday - Flirtations and Fears

Friday, July 14, 2006

I volunteered at the Maritime Museum today, and finally, finally, a man came in who was worth flirting with!

He had come in with a woman. They were working with an environmental action group and wanted to find maps or aerial views of the river bank, and to use the computer to look some stuff up on their way to a meeting. I thought it was cute that he mentioned that they had "met up" to do this research and would have to go back such-and-such a way so she could retrieve her car. He didn't have to mention that. (Like, "Um, just to let you know we don't live together....") I was sure to mention that my late husband and I had attended blah blah, and I mentioned the village I live in (just in case he wanted to look in a phone book or anything like that).

I'm not going to sit around waiting for a call, but it was good practice. He leaned over the counter to read my badge at least three times, it was clear he was memorizing the name, so I might have done something right. I'm rather proud of myself. Flirting is new to me.

I didn't get much else done today, beyond stopping in at the Suzuki dealership to ask what that blank green rectangle on the dashboard display is (they didn't know), and to order a 2003 book. The 2006 book just doesn't make it.

The Hairless Hunk and I spent some time discussing what has to be done with the woods (damn, he's good looking!), and I had nice phone conversations with Daughter (who is visiting Penn State and her old fraternity house for the first time since she graduated), and Piper, and Roman.

The Hunk told me that he had talked recently with the young man who had cleared my woods. I had sold the guy an easement on my property for his electric line, for the house he's building behind mine, for $1 and the clearing of the woods. Coming across my property was about 1/3 the distance compared to coming up from the highway. It turns out that to come across my property requires that they put in another pole at the corner of my lot, and that one pole will cost him $10,000 to have it planted! So it turns out that it's actually cheaper for him to run the line up from the highway, since there would be no poles involved. Ouch! I almost feel sorry for the guy.

I spent a lot of time today reading Israeli and Lebanese blogs (see links on the right. Note - Links will be there on the main page, but not if you are looking only at this post). The contrast between what we hear on the news or read in the newspaper and what these bloggers are saying, is ... I can't think of an appropriate word. If you know what's really going on, the reasons and implications, you might be as frightened as I am.