I wasn't sure whether I'd slept or not. I just knew I'd been tossing and turning for the past few hours, and it was far too hot and sticky to get any sleep. I'd be glad when the summer humidity gave way to the fall not-quite-so-humidity; there'd at least be some respite. It must have been somewhere around three a.m., and just lying here in the dark wondering if I would ever go to sleep or not wouldn't do me any good. Maybe I could go downstairs for a while, find something to occupy my mind. I just needed to make sure I didn't put too much weight on that creaky stair. I unplugged my little e-mail device from the wall charger, automatically, without thinking, cradled it gently in my hands like a treasured possession, and headed for the kitchen. I placed my elbows on the kitchen counter and stared at the coffee pot. I'm quite sure that was the last thing I wanted.
Sunday, August 29, 2010
Connectedness, one year ago today
Friday, August 27, 2010
Bubbalon: Social Ratings, Awful or Awesome?
Parents of kids of a certain age (and teenagers, for some strange reason) might be familiar with the Cartoon Network show Foster's Home For Imaginary Friends. One of the most memorable characters - and, let's face it, when it comes to kids' shows, "memorable" quite often means incredibly obnoxious - and a firm fan favorite is Cheese, who follows the main protagonists around constantly declaring "I like chocolate milk. I like potatoes. I like cereal" over and over and over again; something which kids will quite happily imitate, over and over and over again themselves.
Imagine this: your expressed views could influence the way our current social models work. We are standing on the brink of massive cultural and social changes, and Bubbalon is there to make that leap with you. The old world is based on dictatorship, non-transparency, rigidity and social divide. The new world that we are building on Bubbalon, is a total, complete opposite of that. Each Bubbalonian stands firmly for positive evolution, good social merit, total freedom, responsibility for one's actions, transparency and balance. We are working to make your views MATTER.
Wednesday, August 25, 2010
Book Review: A Spy At Home by Joseph Rinaldo
Monday, August 23, 2010
Getting serious about fitness... this time
Image via Wikipedia
- 10 Ways to Make Fitness Fun! (lifescript.com)
- Exercise can moderate anger: the Mars factor (beliefnet.com)
- Is a Recumbent vs.. Upright Bike Better? (sportales.com)
- Recumbent exercise bike saddle sore? (ask.metafilter.com)
- The Rules to Doing Cardio (slideshare.net)
Nerdy Number Corner: Perfectly Amicable
*Another one of the irregular breaks from the personal drama... it's a math
post, this time around. Have fun!*
a number is called perfect if it is equal to the sum of its own proper
divisors, in other words, all the numbers that divide into it exactly,
including one, but excluding the number itself. For example, the number 6
has divisors 1, 2, 3. 1+2+3=6, so 6 is the smallest perfect number. The next
one after that is 28. A long time ago, a proof was found that every
*even *perfect
number must equal a Mersenne prime, multiplied by the power of 2 smaller
than it. 28, for instance, is equal to (2^2)*(2^3-1), where 2^3-1 = 7 is a
Mersenne prime. At the time of writing there are 47 known Mersenne primes;
hence 47 known perfect numbers, the largest of which having almost *26
million digits*. If even perfect numbers seem rare, it is still not even
known if an *odd *perfect number exists or not, although the many theorems
constructed about its existence suggest that, should one exist it would be
very large and of a very special form indeed. It seems one might construct a little game when it comes to this magical
"sum of proper divisors" function. Starting with any number, we could take
the sum of its proper divisors; then continue with that number; then
continue with that number, and so on. Who knows, perhaps this way we might
accidentally stumble on a perfect number, or perhaps something else. Perhaps
it is best to illustrate by an example. Let us start with the number 20. Its
proper divisors are 1, 2, 4, 5, 10, with sum 22. We will call a number like
20, whose divisor sum is larger, an *abundant number*. 22's divisors are
just 1, 2, and 11, with divisor sum 14. We will call a number like 22, whose
divisor sum is smaller, a *deficient number*. Perfect numbers exist
somewhere between these two extremes. Let's carry on. 14's divisors are 1,
2, and 7, with sum 10. 10's divisors are 1, 2, and 5, with sum 8. 8's
divisors are 1, 2, and 4, with sum 7. And 7's only divisor is 1. End of the
road - 1 doesn't have any divisors except for itself. It takes a little to prove an *iterative* process like the one above,
applying the same function over and over again, has only a limited number of
outcomes. The sequence may stop, such as when it reaches a number which we
can no longer apply, such as 1; the sequence may eventually repeat, looping
over the same numbers again and again in a cycle; or the sequence may go on
forever, never revisiting any previous entries and inevitably visiting
numbers that grow ever larger. It is intriguing to see if there are other
possibilities other than numbers immediately repeating, such as the perfect
numbers, or numbers ending in 1. Perhaps, even if the perfect numbers are
rare, this little trick has something else to offer. 220 is an interesting number. Its sum of divisors is 284, and... perhaps
you've guessed it, summing the divisors of 284 gets us back to 220. Such a
pair is called an *amicable pair* - almost like best friends of numbers,
perhaps? While not easy to find, they are certainly more common than perfect
numbers, and many impressive examples are known to
exist.
220, 284 is merely the smallest such pair, and was known to our old friend
Pythagoras. Discoverers range from Euler and Fermat of years gone by, to
researchers right up to the present day. One helpful thing about amicable
pairs is there is a handy formula for finding the sum of all divisors of a
number (including the number itself), provided you know the number's prime
factorization. Replace each term *p^a* in the number's factorization with *
(p^(a+1))/(p-1)*, and the product now gives the sum of all divisors. An
amicable pair is two numbers *a* and *b*, both of whom have the same sum of
all divisors, *a+b*. In the example, the all-divisors sum of 220 and 284 are
both equal to 504. This concept can be even extended further, you can find
amicable triplets, whose all-divisor sums are equal to the sum of all three
numbers, and so on. Going back to the idea of iterating the sum of proper divisors function over
and over, it turns out we can find some remarkable numbers which eventually
cycle back to themselves in an *amicable chain*. Beginning with 12496, for
example, takes us through 14288, 15472, 14536, 14264 before returning to
12496 on the fifth step. Starting with 14316, it takes 28 steps before we
get back to the original number. Are there any longer chains than that? And,
even if you do not find a chain, are there really any numbers for which the
sequence would go on forever? It's conjectured there are none.
Friday, August 20, 2010
Three Blogging Services That Impressed Me Lately
A little while ago, I ran into this blog about the 5 stages of a blogger's life. I must admit, at the time, I wondered if I'd ever make it out of level 1, in fact, I'm still wondering about that, Shortly afterwards, a follow-up post appeared with a theory about why people stop blogging. To put it simply, it becomes necessary to become a part of a community, to flourish, to realize that the words are not simply being sounded out in an echo chamber. There's plenty of services out there that are chasing you down, offering to help publicize, to link you, to connect you with the rest of the blogging world; however, it might be worth pausing there for a moment. Recently I have tried a couple of services whose initial impressions on me were not good; these are quite well-known services, and among those that spring immediately to mind when you consider blog promotion. Perhaps it was only to be expected that my experience would be unsatisfactory. It occurred to me that the problem with these services was that they were gaining more from me being a member than I was from them; they were getting advertising views for teeth whitening and online gambling venues, while I was getting little or nothing in return except for a great deal of frustration.
- I first heard about Blogger Talk when Rose DesRochers tweeted a link to an article I had written for syndication, reposted on the Blogger Talk site. This was my first experience with article republishing and introduced me to what I discovered was a very strong and healthy blogger community of discussion forums, support, downloads and assistance. The atmosphere is close and friendly; I'll always have Rose to thank for a boost in getting targeted readers to that article and shown me what a difference exposure to the right audience can make.
- Expose Your Blog is in fact a service I discovered while on Blogger Talk. Don Bell was introducing himself in the forums, and Don impressed me immediately with his combination of sincerity and general goodwill to the entire blogging community. Don's site came about after several former members of Blog Explosion were dissatisfied after that site apparently... erm... imploded. Expose Your Blog is reminiscent of the older traffic exchanges where sites are viewed in rotation in exchange for page views on your own site. I must admit I was somewhat dubious about the effectiveness of this, but I have found myself reading and commenting on several of the sites and having that favor likewise returned, so the concept definitely works. if that is not enough, EYB boasts a gorgeous forum and, believe it or not, an online radio station...
- Blogger Luv is a blogger community site in every sense of the word, offering friends and followers like the many social networking sites out there, all with a blogging angle. Bloggers are encouraged to share their sites and experiences from day one, the atmosphere is friendly and good-naturedly competitive, mainly because of the infectious enthusiasm of John Sullivan. If John doesn't poke you in the ribs within the first day of your membership, I'd be surprised. The site's own blog offers interesting stories and articles, but the most fascinating area for me has been the community pages, where links can be offered and voted up much in the way of StumbleUpon or Reddit. This way the community decides for themselves which articles are worthy of sharing, and the articles I have found there have been most useful.
Thursday, August 19, 2010
Darling, I miss you - day 3
Darling, I miss you. Don't worry, it's a short one today. Actually it probably won't get sent today; I may have to finish it tomorrow. My appointment is early in the morning, but I don't know how long I'll be stuck there, so I'll have to check out of the hotel first thing in the morning before I leave. And then, after that, I don't know how much I'll be able to be in touch for the rest of the day. The parking lot is underground; I won't be able to get a signal. More than that, my batteries have to last the rest of the day. I won't get a chance to recharge them after I leave the room. I forgot the cable that let me charge the phone off the computer; I'm not exactly a well-seasoned business traveler, I don't know all the tricks. I've got to let you know what happens with the plane flight tonight; whether I get a seat with my standby ticket. If I don't, I won't be home until tomorrow. And if I do, well, I have to let you know to meet me at the airport. It seems everyone wants to call me on the 'phone and ask what's going on this morning. At this rate, the battery isn't going to last.