Working alongside my grand-nephew Jackson, I glued up the tissue paper collage to the left at the Eric Carle Museum of Picture Book Art, during our Christmas 2013 trip. Since it was so close to my birthday, I considered writing "Age 72" on the picture, but decided there was no need to bring my birthday any closer. After all, I was wearing my "Happy Pig Day" paper hat. Once I'm 72, will I have to put away such foolish things? Nah! After all, as someone once said, "You're never to old to be immature." I think it keeps you young, actually. Perhaps as I grow as an artist, I can master finger painting. 72 is a nice number. Obviously (since it's even), it's not a prime number. Rather, it has the prime factorization 72 = 2 X 2 X 2 X 3 X 3. As a result of having five prime factors, it's evenly divisible by lots of numbers: 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36. Note 1 Of course, it's also divisible by 1 and by itself, but that's true of every integer. My current age of 71, in contrast, is a prime number. That means it's not evenly divisible by anything except 1 and itself. So obviously, once I'm 72, I'll be past my prime (groan). Except then in a year, at 73, my age will be prime again. It's believed that there are an infinite number of "twin primes" like 71 and 73, but nobody has yet been able to prove this. I'm not likely to see another pair of twin prime birthdays, as the next set after 71-73 is 101-103. Although who knows - more and more people are living to 100 and beyond. All this assumes I first make it to 73. If I live to 92, I've already lived 72/92 = 78 percent of my life. Except the trouble with that formulation is that time seems to pass faster as we get older. A year to a child seems like an eternity, whereas a year to someone my age passes rather quickly. Indeed, the last day of October 2013 marked the 10-year anniversary of my retirement, a decade which seems to have sped by. By a commonly accepted logarithmic formulation of this time dilation, my years from 72 to 92 would be, subjectively, only 6.4 percent of my life from age 2 to 92. But this approach is rather suspect mathematically, as the answer you get depends heavily on where you start, and if you go all the way back to birth, you end up dividing by zero. Note 2 Why all this playing with numbers? Apart from filling out my blog entry, it obviously keeps me from having to think too much about actually getting older. Would I ever use this intellectual approach to take my mind off other uncomfortable things that might pop up in my life? My sister Alice used to send me birthday cards with themes such as "Over the hill" and "Old coot". She seems to have switched to kinder cards in recent years. Perhaps being reminded that I actually am over the hill has become a bit too uncomfortable. In addition to being my birthday, Saturday will also be the fourth anniversary of my blog - this entry is #0212. In my initial entry, Introduction: what are these pages?, I wrote, "I'm planning on adding about one entry a week, and I've made a list with enough ideas to keep me going for at least two years." Obviously, I've doubled my initial estimate of two years of material, and I've kept up with my once-a-week schedule. In fact, 212 entries in four years averages exactly 53 entries a year, and of course a year has only 52 weeks. How did that happen? First, I began with eight entries at the release of the blog, to get it off to a good start. Then, for reasons which I can't remember, I posted two entries on a few subsequent dates in 2010 (January 15, February 3, April 8, April 29, and May 6). These extra 12 entries more than made up for those which I missed during the last four years due to vacations. Since in my first four years I've told a lot of my best stories, it's getting a bit harder to keep going. But I've still got a lot of material. And of course, life goes on, so there's more to be told. In the past year, I've devoted seven entries exclusively or largely to baby Darwin, for instance, and she's been mentioned in several other entries. Note 3 My early entries frequently had only a few very small images, or even none at all. Over time, I've started including more and more photos, and generally much larger ones than before. Furthermore, many of them are clickable, taking the reader to an even larger version of the photo. This development has been prompted by the generally faster internet connections available these days. Most people have a high-bandwidth connection such as cable, satellite dish, or fiber optics (such as Verizon FiOS), so downloading larger photos is not a problem. There are some stories I'd like to tell about the family I grew up in that will be best illustrated with even more old photographs. I have boxes (many boxes, and large boxes) of photos from my parents' house that I haven't had time to sort through yet. Other images are on old 8mm and 16mm motion picture reels - these are not so easy to scan. Thus the writing of certain blog entries is waiting for me to locate and scan images from all this material (Margie wants me to go through the pictures so we can then throw some of them out). Other entries are awaiting opportunities for me to take the photos I need to illustrate what I want to write about. I think I'll take the advice I've gotten from several readers, and stop writing in every entry, "You can click on the photo to enlarge it, and then return with your browser's 'Back' button." Most browsers indicate links by changing the arrow to a pointing finger, and that plus the yellow "Tool Tip" containing a title that ends with "(click to enlarge)" ought to provide sufficient notice that a larger version of the photo is available (although you'll only see all of this if you "mouse-over" a photo). Most people by now are well aware of how their browsers operate. Pointing readers directly to a .jpg (an image) violates my general rule of always having navigation information near the bottom of every page, but I don't want to have to embed every single photo in a separate web page. I do think that the quality of my blog entries sometimes suffers due to my determination to keep to my one-entry-a-week schedule, and I've been thinking of posting more irregularly. But I'm afraid that if I drop the once-a-week discipline, my entries might trail off altogether (that's what happened with going to the gym). So I'll keep up with once a week, at least for now. As my 72nd birthday draws inexorably closer, we've received the news that baby Darwin, my granddaughter, has learned to crawl! I'm hoping that watching Darwin develop helps me to slow down the subjective passage of time in the upcoming years.
  Note 1: I hope it goes without saying that every integer factors into a unique set of primes. The divisors of 72 are all the distinct combinations of its prime factors: Note 2: See Logtime: The Subjective Scale of Life. The upshot of the math is the simple formula s' - s = ln(t') - ln(t) = ln(t'/t), where t and t' are start and end clock times, respectively, and s and s' are start and end subjective times. The problem is that if you try to push it back to t=0 (birth), t'/t blows up to infinity. This divergence represents a mathematical statement that the first few seconds of a baby's life must seem to the baby like an eternity. Perhaps this is indeed the case. A 1963 Scientific American article by Clement A. Smith, called The First Breath, is described as "A report on what is known of how a new infant becomes an air-breathing animal". A newly born baby needs to successfully make a rapid transition from getting its oxygen through the placenta to breathing with its lungs, and it had better get this right. [return to text] Note 3:
The entries devoted exclusively or largely to Darwin in 2013 have been: Darwin, Changes, Solid food, Milestones, Applause, Nine months, and First Thanksgiving. [return to text]
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