Category Archives: Science
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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10 Comments | tags: circle, circumference, geometry, pi, pi day, pie, pizza, radius, tau, tau day, trigonometry | posted in Math
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 follow-up 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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3 Comments | 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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8 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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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
Last time I wrote about analog recording and how it represents a physical chain of proportionate forces directly connecting the listener to the source of the sounds. In contrast, a digital recording is just numbers that encode the sounds in an abstract form. While it’s true that digital recordings can be more accurate, the numeric abstraction effectively disconnects listeners from the original sounds.
In the first month of this blog, I wrote about analog and digital and mentioned they were mutually exclusive Yin and Yang pairs (a topic I wrote about even earlier — it was my seventh post).
Today I want to dig a little deeper into the idea of analog vs. digital!
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4 Comments | tags: analog, digital, discrete, infinity, natural numbers, quantum gravity, rational numbers, real numbers, Yin and Yang | posted in Basics, Life, Science
One of the cool things that happened in 2013 is that Voyager 1 has left our solar system. This time it was really, for sure, no kidding! There have been some previous occasions where it left, but this time we really mean it. (Truth is, it’s still way inside the Oort cloud, so in some sense it’s merely left the city for the ‘burbs.)
Say rather that Voyager 1 no longer flies in skies affected by the sun. The heliosphere, the giant fart bubble around our solar system, is filled with our sun’s gassy emissions. Outside that bubble is the galactic ass gas of a billion other suns. Voyager 1, for the first time in human history, samples farts not our own.
It got me thinking about our interstellar golden record: Earth’s Greatest Hits!
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14 Comments | tags: analog, analog recording, digital, digital recording, electrical vibrations, sound vibrations, sound waves, vinyl record, Voyager 1, Voyager 2, Voyager golden record, Voyager spacecraft | posted in Music, Science
As one might guess from yesterday’s post, which was supposed to be about vampires, that the geek force runs strong in this one. Of course, it always does. Far as I can tell, I was born an über-geek and shall remain an über-geek until my final breath (which will no doubt be some geeky observation).
But then geek comes from “carnival geek” and just means someone with expertise in a niche field. I’m fine with that — it’s just the plain truth in my case — but I like to believe my expertise is maybe just a little bit broader than biting heads off chickens. (On the other hand, as perhaps everyone does, I’ve sometimes wondered if joining a carnival might not make for a much simpler life.)
In any event, for a while I intend to indulge my inner über-geek.
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Leave a comment | tags: blog, blog blah, blogging, Chillaxmas, geek, Santa, Santa Claus, Sideband, uber-geek | posted in Computers, Science
Today I’m deep in some POV-Ray project work and waiting to see how the Los Angeles Dodgers do tonight at the St. Louis Cardinals. The Dodgers have a tough boat to row; I think the Cards will have to stumble, and the Dodgers will have to be excellent. For two games. I’d like to see it, but dot, dot, dot. The Detroit Tigers are in similar straits with the Boston Red Sox. It’s looking like the World Series will be red against red.
But due to something that came up in a conversation from yesterday’s article, I’m interrupting my previously scheduled day to bring you this special announcement:
I’m only going to say this once: Global climate change is real.
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1 Comment | tags: Bad Astronomer, Big Blatant Lie, climate change, climate change deniers, Federal Executive Orders, global warming, Phil Plait, President Obama | posted in Rant, Science
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 seemed like an interesting question (given all the people running around these days), so we looked around for a body to help us research the answer.
We just happened to find one handy, so off we all went to the virtual library and math lab. Unfortunately our math consultant was a Communications Arts major and made a small error thinking square kilometers to square miles was the same as kilometers to miles. Fortunately everyone involved obsessively double-checks their work, so we caught the error in time.
Pity, though. The original answer would have been fun to write about.
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15 Comments | tags: big numbers, Earth, Earth population, numbers, square feet per person | posted in Life, Math
Those who know me know that I’m not big on calendar holidays. Even my birthday tends to pass without fanfare. That comes from being single, the island that supposedly no one is. After a lifetime of Christmas and New Years’ being ordinary days, you get used to it.
But I do honor the Solar Event Days because (as I’ve mentioned many times) light is so important to me (and because I’m a geek). Christmas may not mean much to me, but the Winter Solstice does! The days finally start getting longer! Summer Solstice is a day of mourning for the opposite reason.
Today — the Autumnal Equinox — marks the halfway point.
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9 Comments | tags: autumnal equinox, Earth, equinox, fall, moon, POV-Ray, summer, Sun, winter | posted in Basics, Science
Logos con carne 