The whole journey

Now let's walk it slowly, station by station.

1 · A letter becomes bits#

To your laptop, k is not a shape. It is a number: every character has one, and k's happens to be 107. And a number, written the way machines write, is a row of bits: 01101011. That was the quiet magic of Turning waves into numbers: once something is bits, this machine can carry it. (Had you spoken instead of typed, a microphone would have gone first, From your voice to a wiggle, and snapshots would have minted the numbers. A typed letter simply skips ahead.)

2 · The guardians join#

Before those eight bits go anywhere, they pick up an escort. Extra check bits are woven in among them, arranged exactly as Keeping bits honest promised: chosen so that if the trip roughs up a bit or two, the far end can work out precisely which ones and flip them back. The damage hasn't happened yet. The cure is already packed. And even before the guardians joined, the bits were scrambled with a key only your laptop and the router share, because, as Anyone can listen made plain, the whole street is about to receive this. To every antenna but one, your k will be coin flips.

3 · Waiting for quiet air#

The radio does not blurt. First it listens, the good manners of Taking turns: is anyone else mid-sentence on this channel? For a moment someone is. So your laptop waits for silence, rolls its backoff die, counts down its little random pause so it won't collide with every other device that was waiting too, and then, hearing nothing, takes its turn.

4 · Bits become stars#

Now the bits stop being a list and become a shape. They are dealt out six at a time, and each handful of six picks one star from the sixty-four in the constellation of Constellations & 64-QAM: one exact amplitude and one exact phase, chosen together. It's the grown-up form of the flipping games in Bits on the air, leaning hardest on the quiet knob from The third knob: phase. Six bits per symbol if the air is kind. On a rough day the radios agree to a humbler constellation with fewer, farther-apart stars, and simply take a bit longer: The speed limit, being obeyed in real time.

5 · Off the antenna#

Each star in turn now shapes a carrier: a sine wave, the roundest wave there is (Meet the sine wave), wiggling about 2.4 billion times a second, in the very lane the spectrum map of From ripples to radio hands to Wi-Fi. That shaped current sloshes up and down the antenna, and, exactly as Throwing and catching waves described, the wiggle tears free and leaps into the room as a real electromagnetic ripple, off at the speed of light.

Two refinements ride along. The burst is not one pure sine but a whole recipe of them, about twenty megahertz wide, which is what The wave recipe taught bandwidth really means. And that width is no soloist: up close it is the orchestra of carriers of chapter 21, many slow subcarriers standing side by side, each dealt its own patient stream of stars, so no echo bouncing off the walls can smear them. And if your laptop has several antennas, it nudges their phases so the ripples add up toward the hallway, the idea of When waves meet grown up into the beam of Aiming the invisible.

6 · Across the room#

The ripple swells outward like a balloon, and by the rule of Fading away it thins with the square of the distance: twice as far, a quarter as strong. It shoulders through the wall, paying the toll that What stops a wave priced for brick, and comes out thinner but intact. On the way it passes straight through your friend on the couch, and, as Is any of this dangerous? settled for good, it is far too gentle to do anything but pass.

It left the laptop at a fraction of a watt. It arrives at the router about a hundred million times weaker, a genuine whisper, and it lands not in silence but on the ever-present grass of hiss from Where the hiss comes from, standing just comfortably above it. In the very same air, a pair of earbuds is hopping between frequencies exactly as Hiding in the noise described, and nobody trips over anybody.

7 · The catch#

In the router's antenna, the arriving wave stirs a current of almost comic smallness, the catch half of chapter 8's throw. The room's whole roar arrives with it: every station, every gadget, all at once. So the receiver does what Inside the receiver taught: its tuned circuit swings hard for this one channel and shrugs at everything else, and then mixing slides the whole precious wiggle down from 2.4 gigahertz to a comfortable frequency where the electronics can take their time with it.

8 · Reading the knobs back#

Now the oldest habit in the book, in its newest clothes. A crystal set watched one knob, height, in Carrying a voice: AM; A steadier ride: FM watched the speed instead. The router's demodulator watches amplitude and phase together, symbol by symbol, finds the nearest star to each one it hears, and deals every star back into its six bits. The wave has done its job; from here on it is numbers again.

9 · A scar, healed#

And here is why station 2 mattered. Mid-flight, somebody's microwave oven coughed into the 2.4 gigahertz band, and one symbol wobbled onto a wrong neighboring star, so a few of the arriving bits are lies. The guardian bits catch them at once, point to the exact culprits, and flip them back, precisely the repair chapter 19 rehearsed. Noise touched the message, and it did not matter. That one sentence is most of what "digital" means.

10 · The letter arrives#

The bits regroup into 107, and 107 becomes k. The router passes it along to your friend's phone (that second radio hop is this whole story again, told toward the couch), and the letter blooms on their screen. Then comes the part that makes it a conversation: the router immediately sends back a tiny acknowledgment packet, and that ack makes the entire journey in reverse, waiting for quiet air, riding its own stars, fading, arriving. Which is why every piece you've learned had to work in both directions. If no ack comes home, your laptop shrugs and simply tells the story again.

A third of a millisecond, itemized#

The bookkeeping of that trip holds one last surprise. The crossing itself, the part that feels like it should be the whole story, takes about seventeen billionths of a second. Nearly all of that time goes on manners and bookkeeping: listening for quiet air, the dice, the preamble (a little hello of known wiggles at the front of the packet, so the receiver can find the rhythm and lock on before the real bits arrive), the guardians, the ack. The room, it turns out, is the easy part.

The promise, kept#

Back on the very first page of What is a wave?, this book showed you its whole secret up front: three knobs, and no fourth knob hiding anywhere. Everything since has been that promise paying out. Every trick in this book was someone wiggling amplitude, frequency, or phase on purpose, and someone else watching closely to see how the knobs moved. AM was the height knob, FM the speed knob, and your little k crossed the living room riding height and timing turned together, sixty-four stars' worth. Taller, shorter. Faster, slower. A nudge earlier, a nudge later. That was always the whole game.