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L27 and Beyond
Yesterday I introduced you to the idea of words as numbers. There are many ways to create a map between words and numbers. For example, we could assign them the number that represents their position in...
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Square Footage
This one’s mine! So I was conversing with a fellow I know, and the right side of my brain asked the left side, “So just how much square footage per person is there these days?” We both agreed that...
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Sideband #54: Cantor’s Diagonal
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...
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Sideband #55: Numbers & Sets
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....
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Sideband #56: Spelling Numbers
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...
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Here Today; Pi Tomorrow
It’s pi day! Be irrational! Earlier this week I mentioned that “this coming Saturday is a doubly special date (especially this year).” One of the things that makes it special is that it is pi day —...
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Inevitable Math
Oh, no! Not math again! Among those who try to imagine alien first contact, many believe that mathematics will be the basis of initial communication. This is based on the perceived universality and...
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Beautiful Math
Take a moment to gaze at Euler’s Identity: It has been called “exquisite” and likened to a “Shakespearean sonnet.” It has earned the titles “the most famous” and “the most beautiful” formula in all of...
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Moar Math!
But my brain is full! You may have noticed that, in a number of recent posts, the topic has been math. The good-bad news is that there’s more to come (sorry, but I love this stuff). The good-good news...
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Sideband #62: Quaternions
Folded into the mixed baklava of my 2018, was a special mathematical bit of honey. With the help of some excellent YouTube videos, the light bulb finally went on for me, and I could see quaternions....
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Magnitudes vs Numbers
One of my earliest posts was Analog vs Digital. A few years later, I wrote about it in more detail (twice). Since then I’ve touched on it here and there. In all cases, I wrote from the perspective that...
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Rational vs Real
One of the great philosophical conundrums involves the origin of numbers and mathematics. I first learned of it as Platonic vs Aristotelian views, but these days it’s generally called Platonism vs...
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Number Islands
In the Rational vs Real post I mentioned that real numbers were each “an infinitely tiny island separated from direct contact with all other numbers.” The metaphor of each real number as an island...
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“Imaginary” Numbers
Yes, this is a math post, but don’t run off too quickly. I’ll keep it as simple as possible (but no simpler), and I’ll do all the actual math so you can just ride along and watch. What I’m about here...
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“Imaginary” Parabola
Graph of ax2 for diff a values.(green < 1; blue = 1; red > 1) This is a little detour before the main event. The first post of this series, which explained why the imaginary unit, i, is important...
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The Complex Plane
In the first post I explained why the mathematical “imaginary” number i is “real” (in more than one sense of the word). That weird number is just a stepping stone to the complex numbers, which are...
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Parker: Humble Pi
I just finished Humble Pi (2019), by Matt Parker, and I absolutely loved it. Parker, a former high school maths teacher, now a maths popularizer, has an easy breezy style dotted with wry jokes and good...
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Circular Math
Five years ago today I posted, Beautiful Math, which is about Euler’s Identity. In the first part of that post I explored why the Identity is so exquisitely beautiful (to mathematicians, anyway). In...
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Math Books
There are many science-minded authors and working physicists who write popular science books. While there aren’t as many math-minded authors or working mathematicians writing popular math books, it’s...
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