First Order Half life Independence

[Yen Vuong 2I]

Why is the first order half life independent of its initial concentration while zero and second order are? I know that's how it looks mathematically but is there any conceptual basis behind it?

[Rosaline_Chow_2L]

The simple conceptual implication I get is that for first order reactions, the time it takes for [A] to decrease from, for example 2M to 1M, would be just the same as if it were to decrease from 0.5M to 0.25M. Otherwise, I would refer to this post for a more precise answer: viewtopic.php?f=148&t=19614