“Information conservation” is the intuitive idea hiding underneath most everyday uses of “determinism” and “causality.” If a system is thermodynamically isolated - if no matter or energy crosses its boundary, in or out - then all of its future states are encoded in its present state. The future state of the system may be a surprise (to a given observer), but it’s informationally coupled to the current state of the system, so that an isolated system, in this sense, “contains” all of the information about all of its future (and past) states.
Essay 2 of 5. Previously: “deterministic” quietly depends on where you draw the boundary.
I want to sell you a definition. It costs nothing and pays dividends for the rest of this series:
Information is the arrangement of matter and energy in space and time.
That is not Shannon’s definition, and it isn’t trying to be. It’s a functional definition — training wheels, honestly labeled. Later we’ll meet the formal lenses (Shannon information, entropy, algorithmic complexity) and see how each sharpens a facet of this intuition. For now, the point is to make information physical rather than mystical. Stuff exists in arrangements. The arrangement is the information. You can’t have an arrangement without stuff, and you can’t have stuff without it being arranged. Energy and information aren’t identical — but they are inseparable, the way a sculpture is inseparable from its shape.
The sibling of energy conservation
If you’re already comfortable with conservation of energy, then information conservation is the sibling claim: in an isolated system, the arrangement gets rearranged — never conjured, never annihilated. The bookkeeping always reconciles.
Note what this does not forbid: novelty, complexity, astonishment. Those are questions about what the conserved stuff can do, and the answer is “rather a lot.” Conservation is about the books balancing, not about the story being boring.
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Interlude: The Demon Becomes an Accountant
You may remember a certain demon, who found out that its box could not be perfectly sealed. Yet it had one marketable skill: it never lost track of a speck. So it became an accountant. Every evening it audited its box — information in minus information out equals internal change in information — and every evening the ledger balanced to the last bit. “Nothing was created today!” the demon announced proudly. “Nothing was destroyed!” Yet the account book ended at today. He couldn’t balance tomorrow’s books until he knew what tomorrow’s credits and debits would be. Keeping the books, it turns out, is not the same as reading them ahead of time, which is why nobody has ever asked an accountant for a prophecy. Though you could say this much for the demon: its books always balanced — and no prophet in town could claim the same.
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The one question that matters
Draw a boundary. It can be physical (a sealed box) or conceptual (“the solar system,” “the brain,” “the economy,” “this conversation”) — either kind works. Now ask the only diagnostic question this essay needs:
Does anything cross it?
Direction doesn’t matter, by the way. Whether energy leaks in or leaks out, the system and the outside world are in conversation, and the system’s future no longer belongs to it alone. And notice: whatever the internal updating laws are doing, you still have to account for what crosses the boundary, not just what’s inside.
This — not single-valued equations — is what most people actually mean when they say “given the state of the universe at time t, everything else follows.” The folk concept of determinism is really a claim about boundaries and bookkeeping.
The two-way mirror