The Beginning of Infinity, mapped

Not the senses, not authority, not gut feeling, not even our most successful theory. Every one of them has been wrong before and could be wrong now, so nothing is ever settled for good. Deutsch takes this from Karl Popper. Since we can never prove an idea true, or even prove it probable, the one useful thing we can do with it is look hard for what's wrong with it. Knowledge grows by guessing and then correcting the guesses, and a science or a society is only ever as good as its appetite for that correction.

The schoolbook picture of science, gather data, generalize, and a theory falls out, is backwards. You can watch things drop forever and the idea of gravity won't assemble itself in your head. First you guess an explanation, which is an act of invention, and only then do you turn to observation to try to knock it down. That's the mistake in empiricism, the belief that knowledge pours in through the senses, and in its cousin inductivism, the belief that we reach general laws by seeing the same thing happen often enough. The creative leap comes first. Experience only does the filtering.

Put the two foundations together and you get Popper's engine, the thing Deutsch builds everything on. You make a bold conjecture, an explanation you invented rather than one you copied off the data. Then you and everyone else attack it, with argument and with experiment. The conjectures left standing aren't proven; their rivals just failed. That's as close to truth as anyone gets, and it turns out to be enough. The same loop runs in physics, in an honest argument, in a single mind chewing on a problem. Where error correction is allowed to run, knowledge grows. Where it's blocked, things quietly rot.

If guessing is how we get our ideas, what makes one guess better than another? Deutsch's answer is the most original thing in the book. A good explanation is rigid. Every part is doing real work, so you can't move or drop a piece without wrecking how it accounts for what we see.

Take the old Greek story for the seasons. Persephone is dragged down to the underworld, her mother grieves, and the world goes cold. It does predict that winter comes once a year, but every detail is arbitrary. Swap the grief for rage, or six months for three, and the story fits just as well. Because you can vary it freely, it explains nothing. The real account is the opposite: the Earth's axis is tilted, so each half leans toward the sun for part of the year. That forces opposite seasons in the two hemispheres, and you can't tweak any part of it to fit a contrary fact without the whole thing collapsing. That rigidity, not the prediction, is the mark of the real thing.

Here is the strange bonus. When you get an explanation right, it keeps solving problems you never had in mind. Newton worked out gravity from falling objects and the orbits of the planets, and the very same theory turns out to govern distant galaxies and the path of a spacecraft built three centuries later. Deutsch calls this reach.

He's careful about what it isn't. It's not that we assume the explanation will travel, which would be the induction he rejects. It just does travel, because it was about the real thing all along, not about the local case. Reach is why knowledge has no natural stopping point. A good explanation is already pointing past the horizon you found it on.

Some systems improve in small steps and then, with one ordinary-looking change, flip from doing a few specific things to doing everything in their domain. An alphabet is the classic case. Keep adding letters and at some point you can spell every word that exists or ever will, with about two dozen marks. The same jump happened with place-value numerals, with the general-purpose computer, with the genetic code. Deutsch calls it the jump to universality.

The deepest instance is us. A human being is a universal explainer, able in principle to understand anything that can be understood, and therefore a universal constructor, able to build anything the laws of physics allow. A person is the point where unlimited reach begins. That's what the title of the book means.

These two short maxims carry the back half of the book. Problems never run out, because our knowledge will always be infinitely far from complete, so every answer turns up new questions. But every problem the laws of physics don't flatly forbid can be solved, given the right knowledge. The only permanent walls are laws of nature. Everything else that looks like a hard limit, a disease, a shortage, the death of the people we love, is knowledge we don't have yet. It's a deliberately extreme claim, and Deutsch means it at full strength.

This is what Deutsch calls the principle of optimism, and it's a proposition, not a mood. It doesn't promise things will turn out well. It says that whenever something goes wrong, the cause is missing knowledge and not a wall built into reality, that we failed because we didn't know enough, in time.

He fences it off from two errors that often pass for wisdom. Blind optimism is recklessness, acting as if you knew nothing bad could happen. Blind pessimism is the precautionary principle, refusing anything not already known to be safe, which would have forbidden fire. Real optimism is neither nerve nor fear. It's the stance that sends you looking for knowledge instead of gambling or freezing.

Deutsch goes after two humble-sounding ideas and calls them both false, and both small-minded. The principle of mediocrity says humans are nothing special, a smudge on an average rock. Spaceship Earth says the biosphere is a life-support system we must take care not to disturb.

But the biosphere never supported us. Drop an unprotected human almost anywhere on the primeval Earth and they die fast. Deutsch calls it a death trap, not a life-support system. What actually keeps eight billion people alive is knowledge, farming and medicine and shelter and power, all of it made by us. And because knowledge can reshape anything physics permits, the makers of knowledge aren't bit players. We're the most significant kind of thing there is. That's not a license to wreck the planet. It's an argument that the reason to look after it is human, our knowledge and our choices, not a faith that nature is a nurse.