[ItsMe000001]

> the biological signals attenuate with distance from source

The voltage signal is propagated in axons sometimes over very long distances (a meter, e.g. from the foot to the spine). It is renewed (see "Nodes of Ranvier") along the path for as long as needed, at distances that depend on how, or if, the axon is myelinated. That's why the speed is so slow (ca. 120 m/s max., often much slower) - it's actual ion movement through lots and lots of opening and closing voltage triggered channels all along the axons, compared to a purely electrical signal like in a metal wire. This means while in a wire the electrical field is from start to end, leading to electrons exiting on the far end pretty much instantaneously, in an axon am electrical field is only local, and only strong enough to trigger anything for about 1-2 millimeters at best. Then there have to be a new set of channels triggered by the electrical field further up the axon that renew the signal by letting in ions.

Attenuation is more important in dendrites and neuron bodies, spatial distance of simultaneously incoming action potentials (via connected axons from other neurons) plays a role in determining whether a threshold is reached that would trigger firing an action potential from this neuron. Since a dendritic arbor can be quite extensive and have lots of branches location - where exactly along the branches does an incoming signal attach - matters a lot.