Be warned: these next Sideband posts are about Mathematics! Worse, they’re about the Theory of Mathematics!! But consider sticking around, at least for this one. It fulfills a promise I made in the Infinity is Funny post about how Georg Cantor proved there are (at least) two kinds of infinity: countable and uncountable. It also connects with the Smooth or Bumpy post, which considered differences between the discrete and the continuous.
This first one is pretty easy. The actual math involved is trivial, and I think it’s fascinating how the Yin/Yang of separate units versus a smooth continuum seems a fundamental aspect of reality. We can look around to see many places characterized by “bumpy” or “smooth” (including Star Trek). (The division lies at the heart of the conflict between Einstein’s Relativity and quantum physics.)
So, let’s consider Cantor.
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10 Comments | tags: Cantor, Cantor's Diagonal, finite, Georg Cantor, infinity, integers, irrational numbers, natural numbers, numbers, rational numbers, real numbers | posted in Math, Sideband
I didn’t realize it at the time, but by staying up reading until 5 AM this morning, I was awake for the ironically named “Beginning of Summer.” I say “ironically” because the Summer Solstice is the point when the days start to get shorter again. The beginning of summer is also the beginning of the darkness.
Which means that my pagan side mourns the Summer Solstice as much as it celebrates the Winter one. These days, it’s hard not to see a larger parallel in society. Many of us feel and fear society is sliding into darkness — inexorably spinning along a path towards a Winter of Disaster.
This Solstice, as food for thought, I want to introduce The Five E’s…
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10 Comments | tags: darkness, economics, education, entertainment, environment, light, media, punching, rock bottom, social issues, social media, Solstice, summer, Summer Solstice, Sun, Supreme Court, W.G. Sebald | posted in Rant
Voices. It begins with voices. Even before we are born, we hear voices. Human language is the most complex form of inter-species communication that we know. It takes years to learn and many more years to become fluent. Mastering it takes serious dedication and practice.
In the public square, it also begins with voices. The voices of men filled it first. As time marches on other voices are raised: the voices of women; the voices of nationality and race; political voices; religious voices; gay voices; vegan voices and more. Now the public square is filled with the dynamic clamor of many different voices.
To go beyond the beginning, we must listen to the voices.
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12 Comments | tags: listen, logos | posted in Writing

Earl Grey. Hot!
I’ve written about the Yin-Yang of analog versus digital, a fundamental metaphor for how reality can be smooth or bumpy. I’ve applied the idea to numbers, where we see two types of infinity — countable (discrete, digital, bumpy) and uncountable (continuous, analog, smooth). There is also how chaos mathematics says that — the moment we round off those smooth numbers into bumpy ones — our ability to use them to calculate certain things is forever lost.
I’ve also written about Star Trek replicators and transporters, as well as the monkey wrench of the hated holodeck. According to canon, all three use the same technology (which raises some contradictions for the holodeck).
Today, for Science Fiction Saturday, I want to tie it all together in another look at transporters and replicators!
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12 Comments | tags: analog, Captain Kirk, Captain Picard, chaos theory, digital, Earl Grey, infinity, replicators, Star Trek, transporters, Yin and Yang | posted in Sci-Fi Saturday
About 500 years ago a thing happened in Europe: The Scientific Renaissance. It was part of a larger thing, called the Scientific Revolution. These were the seeds that lead to the Age of Enlightenment, when science and rationality were the saviors of humanity lifting us up from the dark ages.
Now the Renaissance is mostly seen as a traveling annual party where people can play Medieval dress-up and eat giant turkey legs (thus proving that anything can be trivialized and you are what you eat). Which is all fine. I enjoy a good outdoor party as much as anyone, and it is interesting finding out what mead actually tastes like.
But I fear we’re forgetting the advances made in the real Renaissance and setting sail back to the Dark Ages.
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Leave a comment | tags: Age of Enlightenment, rational thought, Renaissance, Scientific Renaissance, Scientific Revolution, The Atomic Age, turkey legs | posted in Rant
In 2006 Mike Judge (Office Space, King of the Hill) wrote and directed a film called Idiocracy. It postulates a future 500 years hence when, due to “The Marching Morons” theory, the world is entirely populated by extremely stupid people. In this dystopian future, advertising and commercialism have run rampant in an anti-intellectual culture devoid of intellectual curiosity and thought.
As I watch what passes for communication or discussion on the interweb, as I watch in horrified fascination at the complete failure of nuanced — let alone deep — thought in people today, I begin to realize one thing:
The Idiocracy is here; I live in a world filled with morons.
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24 Comments | tags: Cyril M. Kornbluth, education, Idiocracy, idiots, ignorance, intelligence, interweb, Mike Judge, morons, stupid, stupid people, stupidity, The Marching Morons | posted in Rant
I’ve written several times about the many places we see the idea of a Yin and Yang duality played out in the real world. Even the application of the Yin and Yang concept has a Yin (of true opposites) and a Yang (of thing and not-thing). For example, the opposite of light is not-light, but the opposite of positive is negative.
One of the true opposites is the idea of analog versus digital or, more generally, of continuous versus uneven. Recently I was thinking about the differences between various sports, and I realized there’s a connection to the “smooth or bumpy” distinction I wrote about a while back. Looked at in terms of play, some sports are essentially continuous while others are not.
It turns out that some sports are “analog” while others are “digital.”
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7 Comments | tags: Alfred Hitchcock, analog, basketball, continuous, digital, discrete, football, hockey, MacGuffin, Pulp Fiction, Quentin Tarantino, sports, team sports, tennis, Yin and Yang | posted in Baseball

Happy Twins; Happy Fans!
The Minnesota Twins have had three of the worst years (2011-2013) in franchise history, but this year there have been hints that this year might be different. In April they had a win-loss record of 12-11 (.522) and averaged 5.57 runs per game. The downside was that starting pitchers had a 6.02 ERA.
In May, the pitching got better; starters threw a very good 4.03 ERA. Unfortunately, the bats went ice-cold. Runs per game were down to 3.17, and Twins lagged behind their opponents by 27 runs. The month ended with a 13-16 (.448) record.
June is off to a bang with one of the most exciting wins the Twins have seen in years!
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5 Comments | tags: Brian Dozier, Eduardo Nunez, Josh Willingham, Minnesota Twins, MLB, New York Yankees, Oswaldo Arcia, Phil Hughes | posted in Baseball
Was participating in a discussion about violence against women and wrote a response that’s really too long for a comment, so I thought I’d make a post of it. This is really a comment response, so you might want to read Mark’s post, and the comments there, first.
This response does stand alone and mainly consists of statistics regarding murder and forcible rape. At the end I offer some opinions on the matter.
It’s a heavy, but very important, topic.
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14 Comments | tags: Feminism, forcible rapes, men, murder statistics, rape, rape statistics, rape victims, violence, violence against women, women | posted in Rant
Do you all know the little game to play with fortune cookies? After the fortune, whatever it happens to be, you add the infamous words, “…in bed.” Oddly, this seems to work with almost any fortune.
So I just opened a fortune cookie (sesame chicken…. mmmmm… I just love sesame chicken), and I really cracked up, because today’s fortune reads (this may be one of the best ones ever):
Money will come to you when you are doing the right thing…
…in bed!!
47 Comments | tags: fortune cookie, funny, humor, money | posted in Quotes