Two Billion

In January of this year, the UN's communication bureau noted that the number of internet users worldwide had reached the two billion mark.  That is 2,000,000,000 individuals who are online, surfing the interwebs.  I share that number with you, dear readers, because PK asked a question:

"I have often wondered with this openness if you ever worry about your students or their parents stumbling across it?" 


I "get" the question, and I understand the concern.  Obviously, this blog is not intended for those I teach or for their parents.  It isn't meant for my co-workers or my boss.  Should any of them find this blog, and identify me as the author, the consequences would be catastrophic.  I'm sure there are plenty of other people who could make the same statement...  Writing in this sort of public forum carries risks.

But here's the thing.  I teach math.  I deal in mathematical realities, and I work to help students understand the ways in which math can help us describe our world.  As bloggers of a certain stripe, it makes sense for us to be aware of the risks of what we do, but it also seems reasonable to understand how big or small those risks really might be...

There are about 400 students at my small school.  Most of them have at least one sibling, so figure a total of 800 students.  Add on a couple of parents for each family, and we are looking at about 1600 people.  Let's kick in a few extra just for the sake of an argument and make the math easier in the bargain -- so we'll assume the whole population of people from the school community who might "stumble on" this blog totals 2000 souls.  That would mean that the SET of "my students and their parents" amounts to 0.0001% of all Internet users (that is one ten thousandth of one percent).

Now, this little corner of the cyber universe is a small place.  I don't pull down big traffic numbers, and even if I did, I would still be one of an estimated 266,848,493 websites available to any given user (as of July of this year).  Let's face it -- any one of us is competing with Justin Bieber fan sites and Twilight fan sights and Farmville on Facebook and Angry Birds websites and whatever it is that has "gone viral" on Youtube today.  I've got dozens and dozens of sites linked to this blog, but the truth is that, on any given day, I'm doing well to squeeze in the time to actually visit a handful -- maybe 5 or 6.  So, if we were to assume that the students that I work with have more time to spend surfing the web than I do (after finishing their homework, of course), then maybe they manage to wander around to 25 different places.  That would mean that, in a year's time, each one of them could possibly "hit" 9125 different sites.  Once again, if you do the calculation, that means that each person manages to visit .0034% of all the possible websites.  Put that number together with the percentage of Internet users who actually know me as their teacher (or their kids' teacher), and the likelihood that we are ever going to run into each other at this blog goes to 3 chances in 10 million.

Could it happen?  Absolutely.  Am I going to lie awake at night worrying about it?  I don't think so.

swan

More Tales from the Classroom -- Riddles

Her name, she tells me, means "faith." She also tells me that no one has ever asked her about it... And she looks at me with eyes that are just a tiny bit more open.

"Faith" is a sullen faced African American girl child, and she has that bone structure that points to a royal ancestry. She is lovely, but when I met her, she wore her anger and frustration on her face like the armor one might don for a joust.

Like so many girls, Faith believes that she cannot do math. In her words, she "sucks at math." Just being in math class makes her anxious and fearful and unhappy. I have encountered this before. Many times. Elementary school math teaching tends to favor those who can compute, who learn the "rules" and apply them well, who are quick to process things mentally. Those who need longer to understand, who tend to come at things in some more round-about fashion, who struggle to rattle off the FACTS of multiplication and addition, learn early that they are just BAD at math. It isn't true, but that is what most elementary math education really teaches.

Much of my work, in the 6th grade, is aimed at breaking through that fear, and counteracting the messages that tell them they can't speak this language. We chant and cheer and dance and clap. We play games and we take our partners to the board with us when we work problems. Like contestants on the game show, "Who Wants to be a Millionaire," my kids learn that it is always OK to call a friend.

Things almost always improve while they are with me, but it takes time. The first grading period mid-term progress report may quite possibly show that math is still a challenge, and that is what happened for "Faith." I reported to her mother that she was missing some work, and not participating in class discussions -- not asking questions. Her mother told me that she was confused about how to use the concept of "order of operations," and that she was afraid to ask for help. Mom wondered if she needed to hire a tutor. I told her that I thought that might be premature. I suggested that perhaps Faith could spend 5 or 10 minutes with me at recess, and that we might clear up her confusion, and things would be fine. She said she would suggest that.

The next day, just as we prepared to go out for recess, Faith appeared at my side. "My mom said you might help me with my math," she said. I smiled at her and asked her to wait just a few minutes while I got the rest of the gang out to recess. She found a desk and sat down.

We went to the board together, and worked our way through a couple of examples. Nothing that we hadn't done in math class, but the room was quiet and it was just us. She asked a couple of questions, and we worked a couple of example problems together. She nodded her head and said, "This isn't hard."

I grinned at her and told her, "Nothing is ever hard once you know how to do it. You can always come and find me -- we can do this anytime." She smiled -- the first smile I'd ever seen from her. It made her lovely face light up, and I was thrilled. She went off to recess and I went to eat my lunch.

The next day, just at dismissal time, Faith appeared next to me and asked, "Do you like riddles?" I told her I wasn't very good at riddles, but that I thought they were fun anyway. So she said, "If you are in a room with no windows and no doors and all that you have is a table and a saw, how do you get out." It's a very old riddle, and I'd heard it as a child, but couldn't remember how it went.

"I don't know. Tell me," I said. She grinned and said, "You saw the table in half. A half and a half makes a whole. Then you climb through the hole and climb out."

I laughed out loud and exclaimed, "Oh! It's a math riddle! How wonderful!" She grinned and walked off, headed for home.

Faith. Indeed.

swan

"Poly" Math

I'm a math and science "geek." My earliest college educational endeavors were in engineering, and while I didn't finish that course of study, I remain inclined toward a more technical bent than many folks. I can get fascinated by the far out and esoteric realms of mathematics, and find some of it interesting, entertaining, and philosophically illuminating. I know... strange. Oh, well. Like that is something you didn't already know...

One of my particular interests is the area of study that has to do with transfinite mathematics. Don't panic... I often DO this with my students, so it is perfectly accessible...

Here lately, I've been thinking about the linkage between the theories of the mathematics of "infinity," and the mathematics of polyamory. So, if you want to play on this one, you need to go read a "story." It is called "The Hotel Infinity", and it really is a story. Go ahead. It takes a bit of time to read. I'll wait.

Back now? OK. Then here's how I'm thinking about all of this...

Poly people are fond of saying that "more love makes more love." It is one of those cute, clever, insider slogan-ish bits that we toss off to try and make things sound bright and easy and palatable to all the ones from outside who would look into our lives and make negative judgements. It is right up there on a par with the ubiquitous BDSM slogan, "SSC" (Safe, Sane, and Consensual). It really doesn't mean nearly as much as it seems to on the face of it, and once you start to know a little bit about the reality of things, that quick, glib, clever little throwaway line starts to pale some.

The first problem is that talking about polyamory as if it was a single, easily definable, monolithic thing is really deceptive. There is no one kind of polyamory; no one way of doing it; no agreed upon configuration, or even (when you get down to it) absolute definition of how it really works in every case.

There are poly "webs" where the people involved are really engaging in a tangled set of associated intimate associations. In these relationships, one member may have connections to a number of intimate partners, and each of those partners may have other intimate connections, and so on. The various strands may be only loosely connected to one another, although they may all be aware of the others to some degree or another. It meets the "requirements" for being poly in the sense that no one is being deceptive, and everyone understands that there are all those other connections, but there is little or no intense interaction or connectivity across the various linkage nodes. It really does resemble a big, messy spider web. In such a configuration, if one participant "pulls" on a particular connection, it may impact others within the web, but depending on how far removed they are, they may feel very little of the emotional or relational impact of that "pull."

There are other models for poly that tend to involve fewer members, and form up into configurations that are often "geometric" in terms of how their members relate to one another, and in how we tend to describe them. These are the quads and triads of the poly world. These poly relationships are generally less free-wheeling than the webs. There is often a sort of closed or fidelitous component to these relationships. Within these poly groupings, members may have agreements that allow for the addition of new members through some sort of process that includes input and acceptance from everyone within the group.

There are other models that resemble large families or tribes where members fill roles that are defined hierachically or in levels or pods or some other divisional system that helps to regulate the patterns of the relationship dynamics. Often these groupings have authority structures with power vested in a paternal figurehead who has the responsibility to keep the "family" running smoothly. Offially or not, these groups almost always have some sort of "organizational chart" that defines who is who in the power structure. Often these groups have layers of initiatory paths for new members to come up through as they enter into relationship with the group. People enter in at the lower levels and move up the ladder as if they were joining a big corporation.

And, then, there are the poly folks who don't follow any recognizable patterns; who just do whatever it is they do in whatever way they do it. There are really as many ways of "doing" poly as there are people doing it. We are probably more out of any recognizable pattern than we are truly a real fit in any of the ones I've described. We tend to call ourselves a triad, and that is a convenient and easy descriptor, but it is really about the numeric "count" than anything else.

So, what does it all have to do with "transfinite mathematics?" The Hotel Infinity, remember, always had a VACANCY. No matter how many people showed up wanting a room, there was always space. The odd way the place was constructed, with all those winding hallways, and slanting stairways, and infinite numbers of rooms, meant that there was no end of spaces available. All that had to happen was for the proprietors to get on the loudspeaker, remind the guests that they had agreed to do as asked when the loudspeaker was used, and then tell people to pack up their belongings and move on up to the next room. Not a problem; new guests were simply filled into the rooms vacated when the former occupants did as they were directed. It really didn't matter if you were completely happy in the room with the purple polkadots on the walls -- off you went to the room with the turtle-shaped bed, or the sliding board in the bathroom, or the trap door in the floor... Always room for one more, and anyway, it was an interesting adventure. Just relax and enjoy!

Of course in the story, the person in room #11,943 never knew the person that was creating the necessity for them to move on to room #11,944. They just did what was required and moved. Too, in the end, The Hotel Infinity burned. There was no way to save it. It was too complicated, too many twists and turns. The fire department couldn't find their way down all the winding corridors and slanty stairs to be able to save the place. It all burned to ashes.

That's the fallacy of "more love makes more love." There really are limits in a finite world. There are finite numbers of minutes and finite quantities of energy. One human interaction is not simply interchangeable for another. The striped wallpaper of human relatedness is not equivalent to the elephant shaped bathtub of human relatedness. It isn't all just a wash. We live in a world that is not "infinite." Our relational mathematics is much more often about the simple division of fractions than it is about the stratospheric theorizing of Georg Cantor. When it comes to splitting up the twenty-four hours of our days or the seven days of our weeks or the few fleeting open spaces of our weekends, most of us understand (as we did in kindergarten) that whole is more than half, and half is more than a quarter, and a quarter is way more than an eighth. Further, when we get pushed (arbitrarily) from a perfectly comfortable "room # 27" to a new, and maybe or maybe not so comfortable "room # 28" that is going to create relational disturbance as we pack up all our crap and scramble into the new space. Some folks will appreciate the "adventure" of that routine occasionally -- some won't.

The truth is that human beings fall in love and form relationships in mysterious ways. It isn't like checking into the local Marriott or Red Roof. Sometimes, I get into thinking that the way to make "poly" work easier is to simply go out and find "equivalent" partners. He gets one and I get one. But I'm not built that way. He wants and needs others. I don't. He feels deprived without all those "others." I don't. He wants us to have a family that includes all those infinite whoevers. I can't imagine why we need all the disruption.

But, I'm living here in the Relational version of The Hotel Infinity. The agreement is that when the announcement gets made, all there is to do is pack up the stuff and move on to the next space. Get over it, get on with it, get as comfortable as you can. It isn't personal. It is the way the math works.

That will be part of the work I'll be doing in these next weeks and months -- learning to just be OK with all of that. To find the place where that does not crank me into some sort of frenzy. I understand the intellectual, philosophical, theoretical part of it all. Now I just need someone to help me build the bridge to the other side of the chasm where I won't get wrapped up in my crazy feelings about it all. Then all the infinite others won't be able to make me nuts anymore.

So, there. A list is beginning to form. Things to do with the therapist person. Learn to substitute positive messages for negative ones. Learn to not give a crap about the perceived negative mathematical impacts of polyamory -- just make reactions sync up with the intellectual values. That should at least get us started.

swan