[slewis]

It’s also surprising at first that infinite series can add up to a specific, finite number. If I go halfway to X, halfway again, and so on, where do I end up?

All next realities are weighted based on their probability given the current one. The probabilities are based on our knowledge of the equations of physics. Some realities are more likely than others and adding this all up results in an average outcome. At the smallest scales the average outcome is not actually what happens, but time is a great equalizer.

[osigurdson]

Lots of things are like that. An infinite number of sine waves are needed to make a square wave for example. Taylor series expansion, etc.

[CamperBob2]

An infinite number of sine waves are needed to make a square wave for example.

And even then it only really works if the waveforms are infinite in duration.

Is there a Gibbs Phenomenon equivalent for path integrals?