Head Wrapping

Have you ever tried to understand something, but you just couldn’t quite understand it? Maybe you hadn’t had enough caffeine yet that particular day, or there were too many squirrels playing outside your window, but the facts as they were presented did not make sense to you.

It happened to me with math. In high school, as a junior, I took Algebra II, where we studied (among other concepts), how to graph equations, and that took us into the realm of sin and co-sin, tangent and co-tangent. As a senior, I took Trigonometry, which dealt with polar graph and other stuff. Then I started college, taking Calculus I, and were back to sin and co-sin, but there wasn’t any refresher week to wake up those memories, we just shot off in a whole new direction, and I simply could not wrap my head around any of it.

It happened again today when I thought I would look up ‘quantum entanglement’ and see if I could try to simplify it enough to write a quick blog. The results?

My tummy hurts.

I’m also hungry for cake, and maybe an explanation for that will come in a little bit.

The first article I read was going to ‘simplify’ the concept of  entanglement, and I think it tried too hard. It wanted me to imagine I had 2 cakes. (Hence my hunger for cake.) The cakes were either round or square, either red or blue. In a normal state, you could look at one cake, see its shape and color, but you wouldn’t know anything about the other cake. Let’s say you have a red round cake. The other cake could be red or blue, round or square. You wouldn’t know.

Ahh, but IF the cakes were entangled, you could know that if the first cake was round, the 2nd cake would also be round. But you wouldn’t know anything about the color of either cake, because in the realm of quantum physics, you can’t know everything. Apparently.

Then he moved into round and red being good but square and blue was evil... and I was totally lost. Cake is evil? Never! I don’t care how bad it is for me.

The 2nd article I tried to read was even worse. Not because it tried too hard to simplify the concept, but because it didn’t seem to simplify at all. Or maybe my head was spinning, trying to get a grip on the idea of evil blue square cakes.

So I’ve retreated from the battle, so to speak. I kind of half-way understand the idea of entanglement, but I just can’t wrap my head around the entire concept. I’ve been here, more or less this exact spot, for a number of years. Someday, if I last long enough, I’ll go out and look for another simplified explanation of entanglement.

When I do, I’ll make sure I’ve had enough caffeine, and I’ll close the curtains to keep the squirrels from distracting me.

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!