The Wonders of Math

I love math, from the time I was a small child and it was known as ‘Arithmetic’. The more I used arithmetic to find sums and differences, products and quotients, the more I noticed all the neat little tricks and rules that numbers used.

You know the kind of thing I talking about. 5 times any other number always produces a number where the ‘ones’ digit is either 5 or 0. 9 times any number between (and including) 1 through 10 always equals a number where the separate digits, when added together, equals 9. If you don’t know this little ‘rule’, check it out for yourself. For example 9 X 6 = 63. 6 + 3 = 9. It works until you go past 10, then it gets a little tricky. But I haven’t figured out a rule for 11 through 20, or anything above 10.

And each year, it seemed like arithmetic presented me with new things to play with. Numbers squared and cubed. Square roots. Imaginary numbers!!! Not only would I always do my home work assignments, but I was likely to attempt some of the harder problems that hadn’t been assigned to us, just to see if I could do them.

Eventually, arithmetic became Algebra I, Geometry, Algebra II. I still did all my assigned problems, but now I was attempting the harder problems with the encouragement of my teachers. My one regret from that time was that I never managed to prove the Pythagorean Theorem the way Pythagoras did it. Hmmm, that problem has been simmering away on the back burner of my mind for about 50 hears now. Maybe I should take another stab at it.

My senior year in high school, I was the only girl in 4th year math, known as “Trigonometry and Math Analysis.” I’m not sure where the ‘analysis’ came in at. The entire year was like every other year of math: “This is how you do these problems. Now, on page *, do these problems so I can see that you understand what you just learned.” Somehow, I missed the clues that we were now analyzing how anything in the real world worked.

Then I started college. I was assigned to Calculus I, which I had rather expected to happen. It wasn’t like I had flunked any of my math classes. So try to imagine my surprise to overhear one kid from Chicago complain that he had been placed in pre-Calculus, even though he had taken pre-Calculus in high school. “Oh, you poor kid,” my thoughts went. “How disappointing for you.”

Then I started Calc I. Whoa!! I was not used to taking a class in an auditorium packed to the gills. Or even a half-empty auditorium. And no microphone for the teacher, so it was next to impossible to hear him, particularly since he bulled his way through his entire lecture in a monotone, without stopping to ask if there were any questions or offer any examples. The book I had to pay lots of good money for didn’t explain anything in a way I could understand it. On Tuesday and Thursday, I had ‘homework lab’, where I could ask older students for help with my homework. Inevitably, our conversations went something like this:

Him: This is how you do this type of problem.

Me: But why does that work?

Him: It just does.

Me: When you do that, what kind of a result are  you looking for?

Him: This is how you do this type of problem.

I no longer understood math. It no longer made any sense to me.

To be fair, I was going through some traumatic personal events in my life at that time. So a few years later, I went back to a (different) college to try again. I seemed to make a little headway in Calc I. By which I mean, I caught onto a few references to sines and co-sines during the lectures. The new book - which I again had paid lots of cash for - didn’t seem much better than the first. But mostly I was again just following the ‘rules’ for ‘how to do these problems’, without much understanding of what I was doing, why I was doing it, or what the answer told me.

But I made it through Calc I and Calc II and a couple other math classes. And then... more traumatic life events, and I again dropped school.

I would love to get my degree, just to prove than I can. But I didn’t really want to tackle Calculus again and suffer the same frustration, so I voiced the desire, but never really made any effort to get there.

Have you ever tried one of the ‘For Dummies’ books? My husband and I were recently at our makerspace when my laptop died. Hub wasn’t ready to leave, so I wandered over to see what they had on their reading shelf. And there I found “Calculus for Dummies”.

How hard could it be? Worst case, I wouldn’t understand it, but that was where I was, anyway. So I read the first chapter. And then the 2nd chapter... It made sense! This guy was explaining it in simple terms, reminding his readers of foundation knowledge that they might have forgotten and showing how things fit together.

I had to return the book to the makerspace. Time to get my own copy.

Here I come again, Math!

Trilobite, Do You Bite in Threes?

When you spend a lot of time as a child/teen/adult reading everything you can find on all those fascinating creatures that inhabited the Earth before Humans came along, you come across a lot of strange names. You aren’t sure what those names mean. You might have a rough idea what that type of creature looked like, and that’s probably about all that you know. Because, really, who cares about an extinct sea creature that looked like some crazy kind of beetle?

So I decided to see what I could find out about trilobites, see if there was something about them that would prove interesting. I headed for Wikipedia to get a smattering of layman information before I looked for more advanced info.

Wow. The first sentence in the Wikipedia article is (basicly) “Trilobites ... are a group of extinct marine arachnomorph arthropods that form the class Trilobita. Guess we’d better put on our thinking caps for this one!

Extinct = they are all dead.

Marine = lived in the sea. Or maybe lived in water.

Arachnomorph = ? Well, arachnid is a type of spider, scorpions and what have you. (Thanks, dictionary.com, but why don’t you have the entire word in your list?) Morph has more than one meaning, but the one I’m most familiar with is “to transform”.

Arthropod = an invertebrate with a segmented body, jointed limbs and usually a hard shell that can be molted (discarded) should the creature get too big for it.

So far, what we’ve got is a water creature with a segmented body, limbs with joints and a hard shell. Might have looked vaguely like a spider. What comes to mind is a lobster, but they didn’t really look like that. The most common rendition I’ve seen for a trilobite is an oval shape. The larger ‘end’ is a pretty solid ‘half moon’ shape, with a ‘tail’ that goes down the middle of the oval to the smaller ‘end’. Behind the half moon head and on either side of the tail, filling up all the rest of the oval, are lots of limbs. But other trilobites had much different shapes. Let’s go on; what more can I find?

Trilobites ranged from 1/10 of an inch to about 12 inches. I think that entire range is for adult specimen.

The last of the trilobites died about 252 million years ago. But before that, they were quite a successful species, having spread all around the world and existing for over 300 million years. Scientists believe trilobites started their long journey as much as 700 million years ago, or possibly even further back. And if you think humans have some wildly different lifestyles, you obviously have not met many trilobites. Some were aggressive, and moved over the sea bed as predators, scavengers and/or filter feeders. Others were less aggressive and swam while eating plankton. Scientists are still debating whether or not any trilobites were parasites, while one group of trilobites appear to have had a symbiotic relationship with sulfur-eating bacteria.

Trilobites are thought to have originated in what is now Siberia. But that was over half a billion years ago, and with plate tectonics, who knows where that was actually located? Well, I’m sure there are people who do know, but I don’t. I’m going to have to look it up. Look for it in a later episode.

Anyway, as I said before, the trilobites all died out. Although they seemed to excel in changing shape, habitat and food throughout their long existence, eventually there was only one family left, and when its habitat disappeared, so did they. But while they were here, there were thousands of variations of trilobite. This diversity helped them fill many niches in the cycle of life.

On the other hand, there are some very distant relatives of the trilobites still living on Earth. Think horseshoe crab and others of that ilk.

And that is all I found that I understood in this 29-page article on Wikipedia. Go ahead and read it, if you want, but I warn you, it is FULL of very long words, most of them names of genus, family and specie, but not all. The ones that aren’t are used generously, with no explanation what it refers to, and which may not be in your dictionary. Have fun!

https://en.wikipedia.org/wiki/Trilobite

Check Your Facts

Several years ago, I got an idea for a science fiction short story. It involved the young captain of a ‘worn-out’ asteroid mining ship who found herself pregnant. Such a thing is hardly novel on Earth, but I had the idea stuck in my head - with no idea where I had gotten it - that it wasn’t possible to get pregnant in space. The entire crew is left wondering, “How did that happen?”

Not terribly original, I suppose, but I hoped I was treating the story ‘differently’ from everybody else who had ever written a ‘mystery pregnancy’ story.

So I took the story to my writing group, where everybody told me that of course, she got pregnant; nobody was using birth control, and there’s no reason why people can’t get pregnant in space.

Bummer. That was one of the things that convinced me that my science knowledge was out of date, where-upon I subscribed to and started reading various science magazines, trying to do some catch-up. Until a week ago, I had tried to shove that space pregnancy story out my mind, figuring it had taught me a lesson; Check your ‘facts’.

I was wrong. But not in the way I thought.

Imagine my surprise when I came to an article in the May/June 2019 issue of Discover about how scientists are studying the problem of human reproduction in places that are not on Earth. The problem being that it doesn’t seem possible. Which would make colonies hard to sustain.

As I remember it, they started with lizards and amphibians, which they took to the space station for a period of time. Those didn’t seem bothered by the lack of gravity, or the increased radiation, but some of their off-spring weren’t right.

Then they tried the same experiment with mice, who are mammals, and - biologically - quite a bit like humans. (That’s a lovely thought, isn’t it?) Strangely, the mice must have been freaked out by the no-g or the radiation, or something, but they were not nearly as interested in sex as mice usually are. And even when they did indulge in sex, they didn’t have any offspring.

Apparently, there is a piece of the female mouse’s sexual organs that rapidly decreases and then completely disappears while the mouse is in space. If the same thing happens to human females, then Earth would be the only place where we can make more humans.

Now, that’s a Bummer. But... I was right! (To a degree.) If technology provides a method of humans to begat humans, but only in places that more or less replicate conditions on Earth, then the first human baby conceived without those conditions would indeed be a shock. Not only for the parents, but for the entire race. And that’s the kind of shock I was trying to portray.

So, yes, you should check your facts that you are putting in your stories. And even if everybody in your writer’s group says your fact is wrong, maybe you should check their facts, too.