This doesn't make any sense to me. Isn't this completely backwards? Wouldn't this behavior be expected from a logarithmic knob, and not a linear knob? I know what a logarithmic curve looks like, it rises quickly and then it tapers off, exactly the behavior you describe. But then you attribute that to a lineae knob! The parent comment confuses the hell out of me too, I am just really not putting 2 and 2 together here.

You're missing a critical piece of information. Human hearing (and vision) are logarithmic sensors.

Ears can register sounds from maybe 20-30 dB upwards of 120ish which isn't a factor of 4-6 in terms of power but rather a factor of 120-30=90 decibels or 9 bels or 10^9 or one billion.

Because your ears have absolutely enormous range you need the potentiometer (pot) to have a logarithmic taper to it. The amplifier has an essentially fixed amount of amplification so that's a fixed sound dB output. Your ears can hear a vast range. A linear pot essentially locks the entire output into the same 10 decibels as the amplifier maximum output through its linearity. Once you've turned it to 10% of the range it has precisely 10 decibels worth of range left. If you want to turn the volume down by 40 decibels you have to do that within the 0-10% part of the pot's range.

A logarithmic pot will give you maybe 40-60 decibels worth of adjustment by dividing things up differently. Every 20% of the range increases the output not by 20% but by a factor of 10 let's say. That gives you a pot with a range of 50 decibels which is enough that it roughly matches the absolutely miraculous range of the ear.

"logarithmic" here refers to the number on the scale being logarithmic in the sound pressure level. Restated, power is exponential in the knob value, which roughly matches human perception of a linear increase. An actual linear function is far too slow.

The point is that sound perception is logarithmic. You perceive a 10 times stronger air vibration as twice as loud. So if you have a knob that increases the power that produces the vibrations linearly, you hear a logarithmic increase.

You need a knob that increases power exponentially to hear a linear increase in loudness.