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.
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!
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):
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.
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!
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.
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.
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.