"I'm sure they could eventually piece together most of what I know from the books I left with them, but that still leaves me with a nice headstart."

She smiles, and shakes her head, and almost says something but seems to think better of it. 

"So. Tell me about the fundamental nature of matter as your people understand it."

"Well. In brief, and somewhat oversimplified: matter is made up of parts called atoms, each of which is a specific arrangement of three kinds of smaller parts - electrons, protons, and neutrons. Protons and neutrons are fixed in place in the atom, while electrons can move more freely. The number of protons in an atom determines what type of atom it is, the number of neutrons determines what variant of that type, and the number of electrons determines its electric charge. More electrons indicate a lower charge, because someone started writing it that way a long time ago and now we're all stuck doing it backwards. Electricity is the flow of loose electrons between atoms, and it's a very useful way to move energy around, because under optimal conditions electrons move very fast. Chemistry is essentially interactions between atoms, and the name 'atom' was chosen to mean 'indivisible' because the chemists who discovered them were overconfident about their properties."

"There are types? Do they look different? How do you identity them??

"They're mostly too small to see one by one; you identify them by their behaviour, and by how they look when you have large quantities in one place. Metals, for example, are all made of specific types of atoms—I have a table of all the types in here somewhere—"

He navigates the appendix of the Survey Handbook and finds a periodic table of the elements.

"Iron, type twenty-six. Copper, type twenty-nine. Silver, type forty-seven. Tin, type fifty. Gold, type seventy-nine. And then there's things that are made of more than one type of atom, arranged into molecules: pure water, for example, is an arrangement of two of hydrogen, type one, and one of oxygen, type eight."

"I can in fact tell iron apart from copper," she says gamely. "I think some of our chemists would be able to talk about how this fits our model - they've been on about cycles in fundamental types, it's got to be related - but again, not my specialty. Are the magnets we're looking for going to be visible, or will we need to dig?"

He flips back to the map and zooms in. "A few visible, it looks like."

"Oh, perfect. Maybe we should have gone at night to stop the cousins spying, but I actually can't imagine Curufin stooping to that - not over an engineering problem."

Miles giggles.

"They have principles, just not ones that bear any semblance to -" she sighs. "Magnets. What are we looking for?"

"Magnets!"

He zooms in the display yet further, then toggles the highlighting on and off a few times, causing specific rocks to intermittently glow. "Those. They don't actually do that, my map is just being helpful."

"Wow. Your people are - very gifted and very generous. Can we run one of those off electricity?"

"Yes. If you get enough electricity going, I'll give you this reader, show you how to charge it, and go back across the lake to ask nicely for one of the spares I left there when I went to assault Angband." He pauses. "Also, one of the things I end up doing next time I'm there might be to go through their library and scan all their books into a format the reader can use. I'll need a little help setting that up, for maximum efficiency, I'll want someone to come into my shuttle and write down your alphabet, but once I have that... books can be transferred onto and between readers in seconds, maybe minutes for a libraryful. Once it's on one of them, it can be on any of them."

"You can copy a book in a few seconds?"

"If it's written on parchment or wood or any other physical thing, I can get it onto the reader essentially as fast as I can glance at all the words in order. Once it's on a reader, moving it between them is trivial. Things that use electricity... can take advantage of the fact that electrons are very small and move very fast to put a lot of information in a very small space and move it around very quickly. There's some manipulation of light in there too, because light also moves very fast."

She shakes her head. "That's even better than making them give the books back."

"I'm glad you think so!"

They keep walking. She's actually nearly skipping. "Electricity - am I saying it right? So this flows into all of your devices and makes them light and calculate? How does that bit work?"

"Yes, you're saying it right, and yes, it does. Time for me to oversimplify some more things! So, what happens is that inside the device there are a lot of little pieces of stuff with tiny, tiny carvings engraved in them, and the electricity flows along the tiny carvings, which are specially designed to do certain things. Some of the tiny carvings will react in lasting ways when electricity flows into them in certain patterns, so that afterward using more electricity you can check which state they're in, and that's how the device can remember or record things. As for how you make a tiny carving do calculations - well, how much detail do you want? Until now this was one of the most useless pieces of information I knew, so I'm delighted to explain."

"Please continue. Carvings I can do."

"Right then. Elves count by twelves; my people count by tens; our devices count by twos, because it's simplest that way. So if you want to represent the number three to a device in a place where it's expecting numbers, you have electricity flow into the last two channels in that part of that carving, to represent two and one. Five would be the third-last and the last, to represent four and one. Fifteen is the last four channels, to represent eight and four and two and one. Then calculations are just a matter of designing the carvings so they behave how you want. In the abstract, they're usually made by assembling tiny sub-carvings that each have a useful behaviour: for example, to add two single channels, you use one design that only passes on the flow of electricity if there's some flowing into both of its channels, and another one that only passes on the flow if there is electricity coming into one or the other but not both. You split the channels you want to add, pass one of each into the two 'gate' designs, and what comes out is a representation of zero if both channels were empty, one if one channel was full, and two if they both were. Is this making sense or should I be drawing helpful pictures?"

"Pictures, maybe. I got about half of that."

So he fiddles with his various objects a bit and then draws a simple diagram of a half adder and shows it to her.

"Two channels going in; each can say either 'zero' or 'one'. Two channels going out, which, taken together, will represent either 'zero', 'one', or 'two'; they could do 'three', but there's no way to get three out of what's going into them, you see. Does that make more sense?"

"Yes." She counts it out on her fingers. "Yes. That's brilliant. Who figured it out?"

"I have no idea. It was lifetimes and lifetimes ago, anyway."