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Monthly Archives: June 2014

My mom would have been 90 today. She almost made it, but her path ended three months short of that goal. Last March she found the answer to a question we all have: What comes next? It would be nice to think her lifetime of faith brought the ultimate reward. She surely earned it a million times over.

In any event, she’s at peace now. Those last years were hard — constant pain and a body that no longer served her well or, sometimes, at all. She bore it as gracefully as she did all of life’s travails — always positive, always upbeat. She was the epitome of a wife, of a mother, of a person.

Today, for (what would have been) her 90th birthday, some remembrances.

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8 Comments | tags: 90, birthday, mom, mom is awesome, music teacher, vegetables | posted in Life

This might seem like another math post… but it’s not! It’s a *geometry* post! And geometry is fun, beautiful and easy. After all, it’s just circles and lines and angles. Well, mostly. Like anything, if you really want to get into it, then things can get complex (math pun; sorry). But considering it was invented thousands of years ago, can it really be that much harder than, say, the latest smart phone?

Even the dreaded trigonometry is fairly simple once you grasp the basic idea that the angles of a triangle are directly related to the length of its sides. (Okay, admittedly, that’s a bit of a simplification. The (other two) angles of a *right-angle triangle* are directly related to the *ratios* of the length of its sides, but still.)

However, this isn’t about trig; this is about *tau*!

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6 Comments | tags: circle, circumference, geometry, pi, pi day, pie, pizza, radius, tau, tau day, trigonometry | posted in Math

After three grueling math theory posts (which I’m sure you all read very carefully and are fully prepared for next week’s pop quiz), it’s Friday and time for some fun. Here is a trio of very old jokes about the afterlife. They’re so old they may have gone around the loop to being new again, at least for anyone under the age of *mumble-mumble*.

As I write this post it occurs to me that I don’t hear many jokes anymore. Comedians have stand-up routines, and there are funny quotes, and lots of funny videos and gags and images… Maybe I’m just out of the loop, but it seems like people don’t tell jokes that much anymore. Pity!

I’ll have to look into that. In the meantime, enjoy (and have a great weekend):

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10 Comments | tags: engineers, funny, heaven, humor, jokes, lawyers, St. Peter | posted in From My Collection

We’re still motoring through numeric waters, but hang in there; the shore is just ahead. This is the last math theory post… for now. I do have one more up my sleeve, but that one is more of an overly long (and very technical) comment in reply to a post I read years ago. If I do write that one, it’ll be mainly to record the effort of trying to figure out the right answer.

This post picks up where I left off last time and talks more about the difference between numeric *values* and how we *represent* those values. Some of the groundwork for this discussion I’ve already written about in the L26 post and its followup L27 Details post. I’ll skip fairly lightly over that ground here.

Essentially, this post is about how we “spell” numbers.

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1 Comment | tags: base 10, base 2, base 8, Frederik Pohl, Heechee, irrational numbers, Leopold Kronecker, natural numbers, number bases, number names, numbers, pi, prime numbers, rational numbers | posted in Math, Sideband

In this post I’ll show how Set Theory allows us to define the natural numbers using sets. It’s admittedly a very abstract topic, but it’s about something very common in our experience: counting things. Seeing how numbers are defined also demonstrates (contrary to some false notions) that there is a huge difference between a *number* and how that number is “spelled” or represented.

**Note:** *I am not a mathematician!* This topic is right on the edge of my mathematical frontier. I wanted this addendum to the previous post, but be aware I may misstep. I welcome any feedback from Real Mathematicians!

But go on anyway… keep reading… I dare ya!

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6 Comments | tags: counting, counting numbers, natural numbers, numbers, set theory, successor function | posted in Math, Sideband

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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4 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 | 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 *un*countable (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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11 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