First Sample

We like the phrase “the connectedness of all things.” Here’s a look at what that means.


Most of us like to operate in a little patch of the universe, a bit like a farmer working an acre of land, feeding the family, tending the crops, sniffing out the weather and the seasons, living the comfortable rhythm of a life with a good fence, good water, and good air. Our crops include philosophy, sciences, trades, crafts, and arts. We go to market with our harvests, we return with what we need. It is good.

Along comes the Web. Our fields explode into entire planets, our crops into jungles; our fences fall in tangles with each other; our families take off on wild, scattered stunt flights; our water and air take on colors and shapes and tastes and smells, lurid and tempting; our jungle harvests arise to commit crimes of passion with each other, birthing indescribable offspring; we scrabble, floating in the mighty chaos of change embracing and devouring every one of us.

How do we make our way in such disorder? Douglas Adams characterized the situation nicely in his fiction, when an elderly woman looks out the window during a high-altitude airline flight to see a couple making love on the wing of the plane:

“She was mostly immensely relieved to think that virtually everything that anybody had ever told her was wrong.”

Trying to find our ways, we are making maps of everything, all the time, everywhere, in every way. This is what we call learning. Making maps has become our moment-to-moment obsession as we flounder in the constantly-changing medium of our ‘lifescape’. Once long ago learning was supposed to be a stage of life. Now learning – mapping knowledge for ourselves – is an unending process like breathing or digesting. We don’t stop learning any more than we stop breathing, because the consequences are dire.

Images are maps. An image translates light rays from our world into its own space. The instant we open our eyes for the first time, we begin mapping the universe around us into our eager, overpopulated, infant brains. We annotate our maps with sound, touch, taste, and smell. We adorn our maps with narrative.

We underestimate their power. Here you might get a taste of just how powerful our maps are, all encrypted neatly in our heads. The numbers and scales involved are staggering. We’ll start with two images at the small end of things, deep in the human brain. Out of necessity, we will oversimplify. 

Second Sample

An unusual tour bus driver…


Georg Cantor’s renowned proof of the greater cardinality of the real numbers has been told, taught, and toyed with by any number of mathematicians and writers on mathematics, and here we’ll take a tour through a few of its interesting ramifications. We board the bus, up in a parking lot along a mountain road. The driver’s sign reads “CANTOR”. The driver adjusts a microphone he uses as he leads his tours. Once we are seated and settled he shifts into gear and starts out.

“Welcome to our ascent into the higher ranges of number.

“The critical element to these demonstrations is the very-simple idea of one-to-one correspondence. If you want to see which of two collections or sets of objects is bigger, take one object from each set, pair them up, and set them aside. Do this with all of the objects until one of three things happens (these are the only possibilities, unless you turn into a bored marmot and fall asleep in your seat or go hide in the bus toilet).

“First result: You don’t have any objects left in the first collection to match to something in the second collection;

“Second result: You don’t have any objects left in the second collection to match to something in the first collection;

“Third result: You don’t have any objects left in either collection.

“In the first case, the second collection is bigger; in the second case, the first collection is bigger; and in the third case, the two collections are the same size. The technical term for ‘size’ here is ‘cardinality’: the number of elements (or objects) in a set (or collection).”


Last Updated Thursday, February 29 2024 @ 09:47 am  65 Hits   
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