> Schematics also help explain your circuit because the idioms of drawing them communicate intent.

I think this is a key point. One could imagine three layers:

(1) NETLIST: a list of text-only descriptions, like "R1 1 0 1k", or even a sentence description "connect a 1k resistor between node 1 and node 0"

(2) SCHEMATIC: a 2D drawing with canonical symbols, straight lines for wires, and labels/notes

(3) LAYOUT: a 3D (or multi-layer 2D) physical representation for PCB, or in this case breadboarding

All three layers are useful. (Obviously you need layout to make a PCB, and you need a netlist for simulation.)

But for most humans, where we have 2D visual representations baked in, if you're trying to understand or communicate what's going on:

- It's really really hard to keep track of a bunch of text sentences like a netlist and node numbers/names for all but the simplest circuits -- maybe 3-5 elements?

- It's really really hard to follow a 3D layout of PCB tracks that leads to pads, and then having to remember pin orders etc.

- It's easiest to follow a schematic diagram. It's browsable. It contains "idioms", as you say, about signal flow, logical block groupings, etc.: purpose and intent and functionality, in a way that netlists and physical layouts don't.

FYI, for medium-large digital circuits, I don't think this is true: probably just reading VHDL/Verilog, like reading source code, makes more sense. This is closer to the "netlist" level. I think that's because you'd name modules and inputs/outputs in a way similar to how you'd name functions and arguments in software, which doesn't really apply to "Resistor" or "Capacitor" as primitives.

But for a pretty big practical range of mixed-mode and analog things, I'd argue that schematics really are the easiest level for our brains.

(Disclosure: I'm one of the founders of CircuitLab https://www.circuitlab.com/ (YC W13) where we've been building an online circuit simulator & schematic editor for a long time. Although I'm mostly on the simulation engine / netlist side. My cofounder and other teammates have done most of the schematic GUI work.)

IMHO solderless breadboards still have their place for prototyping some slow circuits, ballpark maybe < 1 MHz signals, if you're aware of the extra capacitance and limitations. :)

"…schematic as data entry for layout style…"

Maybe you can explain.

Are you saying in these cases often the physical PCB layout follows the geometry of the schematic?