Six graders are now required to know the “nets” of three-dimensional figures in their math classes. Have any of you even heard of “nets”? Yeah, there are hairnets and fishnets. There are even dragnets. But this is something unique to math.I know I had never heard of it. Let me kill the suspense and tell you what it is. It is a figure that results from unfolding an n-dimensional figure into an n-1 space. Still confused? Let’s put it another way: If you made a three-dimensional figure with a piece of paper by folding it; then its net would be the unfolded piece of paper.
This is hard to visualize, I know. However the kids are given constructed three-dimensional figures (i.e. pyramids, prisms, cylinders, etc.) that can be unfolded. It is a great teaching aid. They unfold them and see the nets for themselves.
For example, suppose you want to unfold a square pyramid. Here is what it looks like:
If you folded up the vertexes A, B, C, and D, you would have the three-dimensional square pyramid again.
So why should kids know this? I have heard of “thinking outside the box” but this is thinking outside the square pyramid.
Working in the school system with all this new math, has warped my mind. I actually see a reason for this. I will share it with you.
They didn’t teach the Big Bang Theory when we were in school either, did they? Believe it or not all this is somehow related. You see, scientists believe that our Universe was created out of a higher dimension—one that we cannot see or visualize in our minds. I know it is hard to understand, or at least it was for me. Maybe you are smarter.
Let’s go through this concept in baby steps.
Let’s look at the net of a higher dimension. That is possible, you know. We cannot, for example, see a 4-dimensional figure, but we can see its net. This is so because when you unfold a dimension, you see it in the next lower dimension. That square pyramid above was reduced to a 2-dimensional figure using this process. So it makes sense that we could see the basis for a 4-dimensional figure by unfolding it down to a 3-dimensional net. Right? Here’s one now:
This is the net of a 4-dimensional figure called a hypercube. We cannot visualize a hypercube but we can see its net as you see above.
Enough of these baby steps! Let’s get right to the meat of the subject! You know, the Big Bang and how it relates to these nets. Okay.
We want the kids to learn at an early age how to deal with math of things we cannot see. One huge gift of the human mind is to be able to hypothesize and build upon abstraction. Math allows us to do that. We can create geometry well beyond the three dimensions that we can see and touch.
So, as if I have not scared the hell out of most readers already with this new math, let me work closer to the final part of this installment. The current scientific belief is that our Universe was created from 10-dimensions. Further, based on something called the “String Theory”, it is believed that the basic unit of all matter are vibrating strings that freely travel in an out of dimensions we cannot see but only mathematically deal with.
Pretty heavy, huh? Perhaps this is more understandable: For survival, we (future generations projected millions of years into the future) need to travel somewhere off this planet some day and find a new place to live. Speculation is that the nearest candidates would be many, many light-years away by a vehicle moving at the speed of light. We cannot travel at that speed and probably never will even come close. That leaves another alternative: We escape this geometry via another route. Some scientists refer to them as “rabbit holes”. This requires us to understand the shape of the Universe in which we live. Only higher math will enable future scientists to crack this need.
I can remember having trouble with just understanding algebra. I bet you can relate to that too. The future of the human race is in the hands of others. Thank God we older folks don't have to figure it out!
How many of you out there, have thought back about things you wish you had done? It might have been a simple missed opportunity that would have changed your life in some way, or perhaps it is something where you simply made a wrong decision without any life-changing implications. I have found myself doing that from time to time, even though I try to always look forward and not fret about things that cannot be changed. Perhaps it is because I now see my life closing more rapidly and consequently wanting to make sure I don’t repeat mistakes. I am not really sure.
In recent years and at this senior age of my life, I have been working in the school system with young children. Perhaps it is this that causes me to think back to a time when I was their age or younger. Every Monday we have what is called “Advisement Day” where we teachers take the time to talk to the students about behavior and responsibility. Each Monday morning focuses on some word. This past week, the word was “character”, and the week before that it was “bullying”.
I am sure the kids were unaware at the time that I was probably paying more attention to those sessions than they were. Most of them, although participating in the discussions, were simply glad to have their first period math class cut in half due to the advisement sessions. Others were thinking about Spring Break.
When talking about bullying, we stress that the children should not become bystanders. That is, they should not either gather around to egg on the bullying nor should they not try to aid the person being bullied. I was still thinking about that when I prepared for my advisement session to discuss the word character. It made me think back about my best friend Mike in the 6th grade and an incident that happened out on the playground one afternoon during recess. He had bullied another student brutally.
I was a bystander. I was everything that our bullying advisement session tried to discourage, and it showed a really weak character on my part. I found myself wishing I could turn back time and relive that day and done the right thing. Instead. I felt like crap fifty-four years late.
Mike was a popular guy at school. He lived right behind me, so I thought of him as my best friend. He was a natural athlete and was the kind of guy that was always chosen first when a team sport was being assembled. I envied him because he was so good at sports and everyone wanted to be his friend. I usually “went along” with anything he did because I felt his friendship was so important to me.
I am so ashamed of myself for not intervening. To a certain extent, I was afraid of Mike and did not want to get beat up for intervening. However, I had been in physical confrontations with Mike before and knew I could maybe defeat him. So physical threat to me was not a valid excuse. I was more concerned about losing Mike’s friendship and being teased by the other students.
You see, the victim was a girl. Other kids made fun of the girl constantly because she dressed like a boy, looked like a boy, and loved to do everything boys do. In fact, she could hit a baseball a country mile. That is what prompted the incident. We were playing baseball and she asked to have a chance at bat. Mike was pitching. Mike was sure she could not hit his pitch, but she knocked it out of sight. Furious, Mike charged toward her and starting striking her in the face with his fists. Everyone just stood there and watched. He was calling her a freak and a dike. Her nose was bloodied and her eyes blackened. I remember feeling bad for her but still I did nothing. I was more worried about being friends with the bully and not wanting to be teased about the victim being my girlfriend.
I recently received an e-mail from an old classmate. The sender attached a funeral notice saying that the girl had died at age 62. It said she had no children and did not mention a husband. I wonder if I had taken the appropriate action back then would it have changed her life. Would it have changed me in any way too? I will never know.
Should have, could have, but didn’t! I would never stand by today and let a man beat a woman for any reason. I wish I had had the balls to show that character back then too. If there is an afterlife and she is there now, I hope she has forgiven me and everyone else that stood by and simply watched.
