Extraordinary! I woke up at 4:30 am after dreaming. That in itself is not unusual. For years I have been doing that, waking up at odd times of the night, sometimes from nightmares, other times from dreams of longing, or sexual excitement, or violence, and often, fear. It’s hard to get back to sleep after that, even if I need more than 4 or 5 hours sleep. Today was unusual in that there was none of that. I had a teaching dream. I dreamt I was a substitute teacher or guest lecturer at a grade school. I was there with the teacher, whose other appointment had been canceled, so she was there. We were trying to come up something for me to do. I asked about lesson plans and where the kids were in their studies, when all of a sudden I decided to lecture about the number/concept of one. I found a green chalkboard on the side of the classroom, and the teacher had the kids rearrange their desks to face me.
I talked about one, and how, of course, one times something is still one something, how division is just a question of finding out how many of some thing are part of something else. I used the traditional example of one, starting with how many of those ones are there in, for example 25. There are twenty-five. Twenty five times one is twenty-five. But, that is not the whole story. The things under analysis don’t have to be the same. I could have 25 apples and 4 oranges. The question, represented by mathematical symbols, could be how many apples are there in 25 apples and 4 oranges. Well, there are still 25 apples. There could also have been 21 apples and four oranges; 25 pieces of fruit. The question itself has to be defined, and it is, just using symbols. That, of course, led to questions from the students, and more discussion. I spoke of how numbers were originally used to represent philosophical concepts, how useful the number one was to represent the concept of a thing, and other symbols were invented to represent other things under discussion, and how that enabled counting, and the representation of sums, and how zero had to be invented to represent the concept of no thing, or nothing.
I talked of using mathematics to run a warehouse. I gave many examples of ways to understand inventory. I came up with an example of a warehouse that sells two things. One day, the owner had everything in the place counted, but she was only given two numbers: 634 boxes, of which there were 389 boxes of, say, can openers. However, she needed to know how many knife sharpeners she had in stock but everyone had gone home for the day already. So, it’s simple, the students said, you just subtract. Certainly, and many of you can do this in your head, or we can put this on paper, or on the board here: 634, less 389 is 245. 634 minus 389 equals 245. 634-389=245. So there were 245 boxes of knife sharpeners. However, she needed to know how many knife sharpeners she had, not how many boxes of them. Fortunately, she knew that each box of sharpeners contained 24 of them. Then we were back to mathematics, and multiplication. 245 boxes of sharpeners, 24 to a box, so 245 boxes of 24 sharpeners is 5880 sharpeners. 245 times 24 is 5880. 245 X 24 = 5880. “Classic representations of problems, but using symbols,” I said to the students, “that you all know by now.” Simple. But, it could also be represented other ways, using other symbols, for more complex calculations. Boxes could be B. Can openers could be C. Knife sharpeners could be represented by S. 389 plus 245 is 634. C + S = B. This led to more questions, and I went on the show them how this little statement could be even more representative of the actual inventory. It could also be written as say, 15C + 24S = T, or total number of items on hand. So, knowing, at any given moment, how many of each item is available depends on knowing the values of those letter symbols, in this case boxes of each.
I went on to explain how this use of symbols can more useful. I used the same example, but the warehouse had three types of things: can openers, knife sharpeners, and knives. So, we had, on the chalkboard, C + S + K = B. “OK,” I asked, “what if the owner had a similar problem, but had different types of things to be determined. For example, she knew that she had 389 boxes of can openers, 245 boxes of sharpeners, and she did not know how many total boxes she had of everything, but she needed to know how many knives she had in stock. So, using our symbols, C is 389, S is 245, but K is unknown and B is unknown. I asked the students how to solve this problem. They said, just count all the boxes. “But,” I said, “it’s too late to do that, and everyone has gone home. She needs to know, right now, how many knives she has. “She has to work all night, by herself, ” a student offered. Yes, I said, that’s one way, but there are other ways, and it doesn’t solve the problem of telling the manager on the phone, right now, how many knives they can ship tomorrow to the various stores the company has. He has to know, so he knows how many each store gets, and they each want to know today how many to expect. “Can’t be done, ” a student called out.
“But,” I said, “what if she has other information?” For example, what if she knows that for every set of six knives sold, she includes one sharpener. “Could it be done then?” I asked. This riled the students up. Many of them had suggestions, and some said we needed more information. The discussion was lively. The students were engaged in the problem, and things were beginning to click in some heads. Math was no longer esoteric and boring. This is, as I said, a teachers dream. I had opened a discussion, gotten students involved, and pushed them to think. That is what motivates any good teacher. It is what drives some to become teachers in the first place.
Well, this is all very interesting, you say, but, what the hell has it to do with you? You’re not a teacher. What has this to do with Love, and Madness? This blog is about those things, not teachers, not math, not symbols, or the philosophy and use of symbols.
True. But, this is the extraordinary thing. I never dream about such things. I have been caught in a loop of unrequited love, an emotional roller coaster of ups and downs and confusion. My dreams were about her, about the possibilities of life with her, and the impossibility of that ever happening. There was no solution. My marriage broke up, but there was no solution to that, and even that was no solution to my problem. In fact, I was far worse off. My dreams became worse, my sleeplessness increased, my brain spun out of control, and I couldn’t focus, couldn’t think about anything else. I retired. Work was nearly impossible. On my own, I got worse and worse. Depressed. Dysfunctional. Remote. Alone.
Two days ago, I resolved the problem caused by my obsession with Karen. She helped. She told me to lose her address. Finally, a clear message from her. I liked it. It was what I had wanted all along. In fact, I hadn’t been able to resolve my feelings, my emotions, or lack of them. I was stalled out. I no longer felt anything at all, but I didn’t seem to be moving on either. Karen’s message to me hit home. I had carefully avoided being angry with her for any of this. She had done nothing wrong, had always been straight with me and could not be blamed. However, the typical scenario for getting over a lost love, failed marriage, or even death usually involves several steps, of which anger is one. I was angry with Karen now, even though I brought that on myself. For a brief moment, I hated her. I wrote it down. I said, in this blog, “Fuck you Karen.” Never before had I thought such a thing or wanted to direct any anger or negativity towards her. I was wrong, very wrong. That was precisely what I should have done long ago. What a relief! Fuck you Karen, fuck you, fuck you, fuck you. CLICK HERE It was a mantra for me. It worked. For another brief moment, I wanted to die. Seriously, my depression came back full force, and I really, really wanted to kill myself. But, it passed. My head cleared. Logic does not apply to emotions. I would never have solved these equations: Me plus Karen equals happiness, and Me plus Karen is impossible, and Me minus Karen is death, or zero, anyway, nothing. Does not compute.
So, I don’t think the dream meant I wanted to be a teacher. The reality is usually far different from that anyway. I could try being a substitute, bring in a little cash. Hell, the damn retirement board just decided, upon careful analysis of my pension, that they had made a mistake, and I was being given $7.80 more a month than I was entitled to. They sent me a letter, stating that, and the fact that, since I have gotten $7.80 a month too much for ten months, I now owed them $78.00! And the motherfuckers have already deducted the entire amount from my next disbursement. Well, fuck ’em. I’ll survive. My budget was tight enough. Actually, in their complicated math, I will get not just $78 less, but $84.25 less this month. I don’t know how THAT works, since, if I was getting $7.80 too much, then the ten months of that is $78.00, and $7.80 less for the current month would mean I should get $85.80 less.
So, really, I may have to get that part-time job I’ve been dreading. Hmm. Substitute teacher? Always in demand. Flexible hours.