My grandfather believed in an invisible world.

It was populated by angels, demons, and a beneficent God. For unknown reasons God had chosen to avoid being directly perceived by human beings. It had once been otherwise: He had shown himself many times 3300 years ago. Nevertheless, it was still possible to perceive Him indirectly, most powerfully via tracks left in history.

I am an engineer and a computer scientist. My world is different from my grandfather's but, like him, I believe that the world we see is a manifestation of an invisible world we cannot see. My fellow technicians and I share a belief in an invisible world that is no less miraculous than my grandfather's and, many would say, no less evidence of a beneficent God.

To hear about our invisible world, play the child's game of "Why?" Ask an elementary technical question, then ask Why? or What? or How? in response to each answer. After a few levels you're at the invisible domain; another level or two and you're in the spiritual domain. The depth of the stack is a measure of human knowledge. These layers often seem thin compared to a dimly perceived core.

I walked such a path with an inquisitive girl of 13. I was demonstrating some graphics software during a "career day" event and had just closed a window on the screen.

"Where did the picture go?" she asked.

"It's in memory," I answered.

"What does that mean?"

"It means that the picture is now stored in a different way and in a different place."

"OK, where is it?"

I sensed that misty path that lives in the marrow of every technofile.

"Not where, what. It's not a picture anymore, it changed when I closed the window; transformed like a butterfly going back to a caterpillar. It's an arrangement of bits now. The computer broke it into pin head size pieces. It recorded the position, brightness, and color of each piece in a binary code."

"Can I see the bits?"

Drop down into the next world.

"They're stored in CMOS structures. This means they're just below the surface of a few pinkie nail size flakes of shiny silicon metal."

"Show me."

I powered down, opened the case, and showed her the memory chips.

"Show me the little flecks of metal inside the black plastic."

We used pliers to split a spare module so we could see the chip inside.

"You said the bits are just below the surface. If we scrape the surface, can we see them?"

Invisible world coming up.

"Sorry. The structures that hold the bits can be seen, but not the bits themselves."

The teacher came up with a micrograph of the top layer of a memory circuit. They look like very regular cityscapes seen from high in the air.

"Each room in the city holds one bit. A transistor acts as a door to each room that can open to admit millions of electrons."

"Why millions?"

"We can't detect one electron, only whole thunderclouds of them."

"Can I see them?"

"How do you know they're really there?"

"Sorry again. First, the room is never empty. New electrons simply add to a sponge-like latticework of atoms and electrons that's already there. Second, electrons can't be seen. Any attempt to see them changes, in a random way, what you're trying to see. It's like trying to grab smoke."

"How do you know they're really there?"

"By their effects. They're detectable in how they influence other things. They leave tracks; they leave history."

When all is said and done, I'm not so far from my grandfather. It's possible to leap from a visible world we sense, to an invisible one we can detect but never really "see," to one just out of reach of our machinery, but real nevertheless.

The vast majority of the world is invisible. We perceive this indirectly. All of our doings, petty and otherwise, are built on a foundation that runs very deep. We do well to remember, with awe, the worlds that exist just out of sight.