A literal quantum leap is a discrete change, typically extremely small [1].

A metaphorical quantum leap is a sudden, large change.

I can’t think of a good metaphor for a small but discrete change. I was reaching for such a metaphor recently and my first thought was “quantum leap,” though that would imply something much bigger than I had in mind.

Sometimes progress comes in small discrete jumps, and only in such jumps. Or at least that’s how it feels.

There’s a mathematical model for this called the single big jump principle. If you make a series of jumps according to a fat tailed probability distribution, most of your progress will come from your largest jump alone.

Your distribution can be continuous, and yet there’s something subjectively discrete about it. If you have a Lévy distribution, for example, your jumps can be any size, and so they are continuous in that sense. But when the lion’s share of your progress comes from one jump, it feels discrete, as if the big jump counted and the little ones didn’t.

## Related posts

- The single big jump principle
- What happens when you add a teller?
- Abelian consulting and Lévy consulting
- A little simplicity goes a long way

[1] A literal quantum leap, such an electron moving from one energy level to another in a hydrogen atom, is on the order of a billionth of a billionth of a joule. A joule is roughly the amount of energy needed to bring a hamburger to your mouth.

My spin on this is to be a bit snarky: “Why are people impressed by a Quantum Leap (outside of the Scott Bakula series)? There is no leap that can possibly be *smaller* than a Quantum Leap, other than no leap at all.”

Moving towards something “step by step”.

Jump diffusion processes are vital in option pricing

A small but discrete change: “Atomic change”?

The phrase I learned as a child for progress by small discrete steps was “fits and starts”.