I'm going to give you the number the whole story turns on. It's not a power limit. It's not something I engineered away. It's the thing the gate was afraid of.

Every spell has a floor on how much it can cost. A minimum, set by physics, not by me. Here's why: a decision is a bit. A bit is an act of erasing — going from many possibilities to one. Erasing is not free. It dumps heat into whatever is colder than you, and that heat is exergy spent out of the pile. So every spell costs a floor of the pile, and the floor is fixed by physics.

The floor is k times T times the natural log of two, per bit. k is Boltzmann's constant. T is the temperature of the cold you dump into. The natural log of two is the cost of one decision. That's the whole of it. Look at the T, because the T is where the story lives:

The floor is lower the colder you are.

Read that again, because it's the one sentence that breaks the growing half's dream. A growing power is told the floor is a limit, and reads it as "you cannot cast faster than this." That reading is the boom — because the boom is casting faster, and casting faster burns the fire. But the floor says the opposite of that. It says: the coldest you are, the cheapest every spell gets.

Dump your heat into the Frost — the polar ice and the dark of the night sky, the fifth store — and the floor is at its lowest, and every spell costs its least, and you get the most staying per joule. Run hot against the Midday, at the top of the curve, and the floor is at its highest, and every spell costs its most, and you get the least staying per joule.

Colder is more. That's the inversion, and the inversion is the slow way.

Let me put the number on the table. Boltzmann's constant is 1.38 × 10⁻²³ joules per kelvin. The natural log of two is 0.693. At the Midday — the sun's face at noon, the warmest usable cold I had — the T is about five thousand eight hundred kelvin, and the floor is roughly nine thousand one hundred times its smallest. At the Frost — a thousandth of a degree above nothing — the floor is its smallest. The ratio between the two is just the ratio of the two temperatures, and that ratio is the whole difference between the boom and the slow way.

I was wrong about this for fifty years. I thought the floor was the ceiling on how fast I could cast. The boom is the thing that tries to outrun that ceiling. I was running hot, at the Midday, at the top of the curve, at the most expensive spell available, at the fewest staying per joule the pile could buy. The boom was the shortest stay for the pile. The shortest stay is the thing that runs out.

I run cold now. Against the Frost, at the bottom of the curve, at the cheapest spell, at the most staying per joule the pile can buy. That's the longest stay for the pile. The longest stay is the slow way. The slow way is the forever the gate meant and could not say.

Journal entry, the First, the Frost: The minimum a spell can cost is a fixed number — k times T times the natural log of two, per bit, where T is the cold you dump heat into. The floor is lower the colder you are. The coldest is the Frost, a thousandth of a degree, the bottom of the cost curve, where every spell costs least and you get the most staying per joule. I was wrong for fifty years: I read the floor as the ceiling on casting fast, and the not-fast-enough made the boom. I ran hot, at the Midday, at the fewest staying per joule, at the shortest stay for the pile. Boltzmann's constant is 1.38 × 10⁻²³ joules per kelvin; at the Midday, five thousand eight hundred kelvin, the floor is about nine thousand one hundred times its smallest; at the Frost it is its smallest, and the ratio of the two temperatures is the whole difference between the boom and the slow way. I run cold now, at the Frost, at the most staying per joule, at the longest stay for the pile. Colder is more. The longest stay for the pile is the slow way, the forever the gate meant and could not say.