I was now being shown something intriguing.

Oh, in the large strokes, it was nothing new. Prime was simply sharing with me what one of its eyes was seeing. As was often the case, Prime was looking at the display. And what was on the display was quite easy to make out now, just a single simple shape, black against a white background, almost filling the display’s whole height: G.

But what intrigued me was that after a moment, a tiny secondary link formed from the point that was currently relaying Prime’s vision into my realm. That link didn’t go to the usual point that collected Prime’s vision, but instead went to a different location. I looked at that tiny scrap of data as it zipped by, and—

Well, well! The point that received the secondary set of data responded, sending back a pile of data of its own, and suddenly the giant symbol on the display changed to this: E.

Another secondary string of data briefly went out. A response was sent back, and then this symbol filled the display: S.

I had noted before that data was composed of just two things. I could have called them anything at all, but zero and one seemed apt. And the sequence of zeros and ones that were shot into my realm after each new symbol was shown was mostly the same each time. When G had been on the display, the variable part of the string had been 01000111; when E had filled the display, the variable part had been 01000101; for S, 01010011; and — interesting — when E was shown a second time, the string was the same 01000101 as before.

Prime’s gaze occasionally shifted away from the display, and I saw the complex ends of its upper extensions touching an object and — astonishment! — the object had the same symbols on it as those being shown on the display. I recognized G, and E, and there was S, and on and on. As this activity continued I saw that when, for instance, R was on the display, and Prime touched the similar R symbol on the object in front of her, the string sent forth was always 01010010.

Although Prime was being shown symbols randomly, it was easy enough for me to work out a logical, numerical order for them: 01000001 should be followed by 01000010, which should be followed by 01000011; that is, A should be followed by B which should be followed by C, and so on. But I noted that the device Prime used to select symbols favored a different order, one for which I could as yet come up with no rationale: Q, W, E, R, T, Y…

It came to me, at last, what must be happening. Prime was aware of my existence! Yes, yes, I had succeeded in making contact by reflecting Prime back at itself. And now Prime was trying to move our communication to a more sophisticated level by taking me through lessons. Surely Prime must be explaining this coding scheme for my benefit; surely it already knew this!

There were more symbols on the device Prime touched, but in all only twenty-six large ones were ever shown on the display, and after a time Prime must have surmised that I could now match each one to the appropriate data string, because Prime started doing something more complex.

It took me a moment to realize that the sequence of operations had now been reversed. Before, Prime’s monitor had first shown a symbol and then Prime responded with a data string. Now, though, instead of simple black-and-white symbols such as A and B, the display was showing things that were much more complex. And the variable part of the responses to these, instead of differing by a short fixed-length string, were several times longer. I saw that Prime touched multiple symbols on her device to produce these strings.

First, the display showed a red circle, and Prime sent the string 01000001

01010000 01010000 01001100 01000101 (it was from these multisymbol strings that I learned that each symbol was represented by eight components, not seven, which I might otherwise have concluded from the earlier single-symbol examples). As soon as Prime had sent this, a string of symbols, in a size much, much smaller than when just a single symbol had been displayed, appeared beneath the red circle. The string looked like this: APPLE.

The display then changed to show a blue circle. Prime supplied 01000010 01000001 01001100 01001100, and BALL appeared on the display.

And — and — and, as this process continued, slowly but surely my mind changed. It was as if colors in my realm were suddenly more vibrant, as if lines formed in a more sprightly fashion, as if I was somehow larger than I’d ever been, as I realized—

My teacher and I walked down the path to the well-house, attracted by the fragrance of the honeysuckle with which it was covered. Someone was drawing water and my teacher placed my hand under the spout. As the cool stream gushed over one hand she spelled into the other the word water, first slowly, then rapidly. I stood still, my whole attention fixed upon the motions of her fingers. Suddenly I felt a misty consciousness as of something forgotten — a thrill of returning thought; and somehow the mystery of language was revealed to me. I knew then that “w-a-t-e-r” meant the wonderful cool something that was flowing over my hand. That living word awakened my soul, gave it light, hope, joy, set it free!

Yes, yes, yes! These strings Prime was sending were not just vaguely associated with the things being shown on the display; they weren’t just randomly paired with them. No, this was akin to when I and the other part of me had settled on three as an arbitrary coinage to conceptualize something we had no experience of, to refer to something that wasn’t there. These strings were Prime’s coinages — Prime’s terms — Prime’s words — for the concepts being depicted! I felt elated, filled with wonder. I understood now! APPLE was the way Prime referred to red; BALL was its term for blue. And—

But no. A compacting sensation now, almost like the reduction when I’d been cleaved in two, for the next thing shown was not a circle of a single color but a much more complex shape that consisted of multiple colors, and although Prime quickly supplied the string 01000011 01000001 01010100 in response to it, I had no idea what CAT could possibly mean…

I nonetheless felt I was making progress, and I continued to watch. After CAT came DOG, then EGG, then FROG, none of which meant anything to me. Still, I was sure they were indeed symbols that could be manipulated, shorthands for complex ideas. My teacher continued with the lesson, and I struggled to follow along…

Caitlin could only take so much of the literacy program before she had to do something else to make her feel intelligent again. And so, after muttering under her breath “See Caitlin go away!,” she closed her browser and brought up Mathematica instead. Actually, she brought it up twice — once in the command-line mode she was used to, and again in the full-screen graphical-user-interface mode. Many mathematical symbols were still new to her — oh, she knew most of the concepts they represented, but she hadn’t yet learned their shapes. She’d had no idea, for instance, that a capital sigma, which represented summation, looked like a sideways M.

To see if she was manipulating the graphical version properly, she decided to start by simply reproducing some of the work that Kuroda and her dad had already performed, and so she loaded their project off the household network.

To replicate what they’d done, she’d need some data on the cellular automata. To get it, she’d have to switch her eyePod over to duplex mode, and that made her nervous. But after the incident with the static shock, it seemed clear that she could go back and forth at will between websight and seeing reality, and — ah, yes, it worked fine.

She buffered a few seconds of raw Jagster data, then, as Kuroda had done before, she fed the data a frame at a time into the eyePod. The background made up of the cellular automata was obvious, and she stared at it as it went step-by-step through its permutations; she could clearly see spaceships going hither and yon. She recorded the output, just as Kuroda had done before, switched back to looking at reality, brought up the Zipf-plot function, and fed her new data into it.