Lovely thinking

i carry your heart with me

by ee cummings

i carry your heart with me (i carry it in
my heart) i am never without it (anywhere
i go you go, my dear and whatever is done
by only me is your doing, my darling)
i fear
no fate(for you are my fate, my sweet) i want
no world(for beautiful you are my world, my true)
and it's you are whatever a moon has always meant
and whatever a sun will always sing is you

here is the deepest secret nobody knows
(here is the root of the root and the bud of the bud
and the sky of the sky of a tree called life; which grows
higher than the soul can hope or the mind can hide)
and this is the wonder that's keeping the stars apart

i carry your heart(i carry it in my heart)

This is my wife's favorite poem. I wish I had written it.

Glassy thinking

My sister Gillian thinks in glass. I don't know how she learned to do such a thing. It is a mystery to me that she can think in glass, that Owen can think in sound, that Bruce can think in words, that Crystal can think in dance. These things are inconceivable to me, and I take such great pleasure from them.

Glass is most... I was going to say it's unusual, but in fact it is nothing more than a very accessable form of a very common substance, sand. It is colored by the addition of various elements. Gillian can tell you what they are, but I'm thinking cobalt for blue, copper for green, gold (I think) for red. It takes the breath away.

Beyond the science of it is the magic of it. Gillian's right brain formulates some sort of vision of something, god knows what. She uses her left brain to work out what glass to put where, what colors will transform into what light, what light will transform into what beauty, what beauty will make the heart sing. And she puts it together, exposes it to tremendous heat and it works.

That's about the weirdest thing I can imagine. Who worked that out? How did she? She's my older sister, made her living as an avionics engineer, raised a passel of kids, loved me because that was her nature.

We went to a strange boarding school together when she was about 13, me about 11. In London, SW something-or-other. It was a horrible school. The Latin mistress was a predatory lesbian who spent too much time in the girls' dorm, the English master a predatory creep who spent more time with me than was good for me. The boy's dorm-master was a strange and sadistic man, and Gillian's room-mate howled at the moon, no kidding, for real, for hours and hours. It was there that Gillian and I became friends, working our way together through some very, very strange growing-up experiences. Neither of us emerged entirely unscathed, but we emerged together, alive together.

Like fused glass, elemental but changed, hardened in some ways but still brittle and vulnerable in others. Now she lives in Mexico and thinks in glass. She is amazing, quite beyond my ken. I wonder if we are one as we used to be or if time has, in fact, separated the elements.

Vanishing thinking

Things vanish. Sometimes they fade away, sometimes they simply vanish.

Sometimes they vanish because we stop seeing them. Vanishing, in such a case, is something I did, not something it did. For an example of this click the title of this blog, "Vanishing thinking," and you will vanish. You'll discover yourself somewhere else most interesting. Stare at the cross for a while and relax. Reappear here when you're finished.

I am curious to know about the present, meaning the thin wedge of time that is this very instant, the tiny time-wedge surfing down the wave made by the colossal event of the future colliding with the past. The past is huge, goes back a long way, is filled with lots of stuff, like the ocean below. The future seems infinite, everything possible is stored there waiting for its chance to be, like the sky above. The wave is just a surface that separates the two, and it has no dimensions of its own, no material to call its own.

The present has no dimension, it is the translation from "will be" to "was", and then it vanishes to be replaced by some next instant. Where did it go? Will it be okay? Who is experiencing it now that it's gone? It wasn't is for nearly long enough, I want it to linger with me a while...

What about the instants coming towards me at the speed of light? Who is experiencing them before I do? Do they vanish for those creatures in the same way mine will vanish for me after will becomes is becomes was?

What are all these instants running from in such headlong haste? Why are they so desperate to slip away, to vanish?

Or is it not the present that vanishes at all? Is it something I'm doing or not doing that makes me think it vanished? Is there some funny analog of a green dot moving around erasing not the dots, but my ability to see them?

That would be weird, if that time I beat that kid up because he had a steel plate in his head is still happening. If he is still screaming and screaming and I am still hammering on him forever and ever, just an instant away and not visible. Me unable to stop punching him, unable to stop loathing myself for doing it.

Another thought: Is my heart still broken?

Is hers?

Let it vanish, after all.

Math-magical thinking

Click on the name of this post, Math-magical thinking, and it will take you to a web page that will amaze you.

Do not read any more of this posting without examining the page and trying it out.

Surely it is magical!

Now let's do the required numerical thinking, not to diminish the magic of the webpage I sent you to, but to increase the magical-ness of math.

Any two digit number has two digits, call the first "x" and the second "y". When we place them together to form a two digit number, as in "xy", the value of the number itself is 10x + y. This is the difference I referred to in an earlier blog, the differnece between a number, and the quantity it represents. (Not all numbers do that, by the way)

"82", for example, is ten 8's + 2. Similarly "xy" is ten x's + y. We write that 10x + y.

So you made up a two digit number with the value 10x + y.

The puzzle now asks you add the two digits together. That give us a second number, x + y.

Finally you are to subtract the second number from the first, giving:

(10x + y) - ( x + y)

When you simplify that expression you are left with 9x. In other words, no matter what two digits you choose to use, once you perform the steps outlined, your final answer will be exactly 9 times larger that the digit you used for x, the digit in the tens place.

Which means that every possible answer is a multiple of 9. To whit 9, 18, 27, 36 and so on. No other answers are possible.

If you go back to Math-magical thinking link, look to see what symbols go where, and in particular notice the symbol matching multiples of 9.

That's math-magical thinking. Math is very, very cool.

Binary thinking

Do you remember the guessing game you may have played as a kid, where one person thinks of a number between 1 and 100, and the other person has to guess the number in as few guesses as possible? It's a great game to play with kids because after a while they begin to figure out, all by themselves, how to do what compter programmers call a binary search. It's an elegant piece of thinking that a kid can invent as soon as she understands how numbers are built.

If the kid guesses 67, and the number is 14, you say, "Too high." She may say 66 next guess, then 65, but after a while she'll figure out that counting down one at a time is boring and she'll get more adventurous.

If you play it in a way that keeps them interested, for example by having two kids compete to see who can accomplish the task in the smallest number of guesses, the loser being fed to the sharks or something, after a while they'll figure out that there is a "trick" beckoning them and they'll begin to hone in on it. The trick is to do a binary search, that is keep dividing things in half. Guess 50 first. Higher? Guess 75. Too High? Guess 62. And so on. If you do this you will always be able to get the right answer within 7 guesses.

Increase the upper limit of the game to 1000, which would be stunningly boring without a binary search. With 1000 you can nail the number within 9 guesses, every time. 10,000 can be cracked in 14 guesses. A million, not that I recommend it, can be cracked in 21 guesses max.

Segue from 21. Another great game, although not binary in nature, is the 21 game. One persons starts and can say 1, 2 or 3. The second person can add either 1, 2 or 3 to the number the first person said.

So I said 2, and you could say either 3,4 or 5. Suppose you said 5.

I can say 6, 7 or 8. I say 8. You say 11. I say 13. You say 14. I say 17, You say 19. I say 21.

Because I said 21, I win. You get fed to the sharks. Play the game a few times and a light will go on in the child's head - you can see it happen. She'll figure out that whoever says 17 will win. Keep playing, another light will go on. 13 is the magic number, because she who says 13 can say 17... And so on.

It's better to do this with a group of kids, otherwise you're just whupping some kid's ass over and over again and after a while she'll begin to resist. But if there's a bunch of them playing they have fun and whoever finally beats you feels like a champ.

I start every game with the question, "Would you like to start, or would you like me to start?"

When a kid says, "I want to start," and then chooses the number 1 in a strong voice, I know I'm shark bait.

Serendipitous thinking

I don't know who took this picture but I find it endearing as well as intriguing. But it is the way I found it that I wish to discuss.

I stumbled upon it.

There is a link on my blog to http://www.stumbleupon.com/. It's like Google only when you click on Stumble Upon it takes you randomly across the web. Well, not entirely randomly. It first asks you what sorts of things you'd like to stumble upon, and then off you go. It was invented by some Calgary boys, go Stampeders! So it's like a search engine but fuzzier and a lot less predictable, which is its whole point.

Is it cheating to program a machine to provide seredipitous events for us? Inside me somewhere there is a cranky old man slapping his forehead and saying, "My god, just live your own life, will you? Discover your own ladybugs in curious juxtaposition with waterdrops and daisies. Don't have some machine doin' it for you!" (Ageing hippies, do those words sound at all familiar?) But responding to the cranky old man is another voice saying, "Yeah, but... what does curious juxtaposition mean?"

And then adding, "One more word and it's the dumpster for you, old man!"

Serendipity comes to those who put themselves in the position to stumble upon it.

Zero thinking

I did a Google search for "zero" looking for a good graphic. "Zero" produced 252,000,000 hits. Two hundred and fifty two million. That's a lot of hits for nothing.

Those who read my earlier post, "Numerical thinking..." may be reaching for a calculator. Well done. For those who didn't, it would take me just under eight years to visit every one of those sites, one per second, 24/7. So I visited them all and none had a good graphic.

The correct graphic is not a graphic of nothing, but is no graphic at all. I hate that.

This is interesting - an African Grey parrot named Alex gave consistent, verifiable evidence of its ability to grasp the concept of "zero" as being meaningful in itself, not just as identifying an absence. I went out and bought an African Grey parrot right after I learned that. I explained to my wife that the parrot was a Christmas gift for my dog Vinnie, and she laughed in a way that said, "I'm not stupid, but I love you... Maybe I am stupid." She's very loving, I think.

So I have this African Grey parrot and I have a concept of zero. How to move my concept to the parrot? There's the rub. Along with, why bother? Because if I can teach it, I will know it, and right now I feel like I'm just faking that I know it. This is why I teach - so that I can know.

The direct face of zero is nothingness. Multiply any number, no matter how huge, by zero and you wind up with nothing. Zero is the great destroyer. The underbelly of zero is infinity. Divide any number by zero and you get... well you don't actually get anything, but "not anything" in this case is the opposite of "nothing." Dividing by zero is asking the question, "How many groups of zero are there in this number?" You can't say zero, because obviously there are more than that. A million? More than that... A trillion? More than that... A really huge number of zeroes lie inside every number, an infinitude of them.

Where's that damned parrot?