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Comment by sushisource | Hacker News Reader

Log scales aren't intuitive to humans. I think it's a great example because that's sort of what it tricks you into doing.

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I guess we don't count in log scale. The billions of people on the world will never get millions, only thousands, hundreds, and tens.

Give a person a meter and they'll take a kilometer. Ehh?

One would think it would be since we hear and see in log scale.

Yes we hear in log scale, but why would that be intuitive? Ask someone how loud or soft any sound is - a dog bark, a cymbal crash, a whisper - and you won't get a numeric response. We're used to measuring distances, weights, etc but not volume, aside from the volume knob which goes from 0-100%, and the logarithmic scale is already built in

Assigning an absolute number is much more difficult than assigning numbers on the relative difference between things.

Just take the use of dB in acoustics or the magnitude system in astronomy.

Both dB and the magnitude system have nothing to do with difficulty, and everything with practicality. The dB scale is defined in terms of air pressure, which runs on a linear scale.

What does that mean? I wouldn't say we hear in any scale. Log scale is an academic construction, it makes things easy to think about, it's not a physical property of hearing or seeing.

The linear scale however is a physical property of the world (photons per seconds for example) and if we change the intensity in a linear way we notice that the perceived change is not linear, but logarithmic. Hence volume or brightness controls typically aren't linear but logarithmic - people want it to change linearly instead of not at all at the one end and a lot at the other end.

The root of the magnitude system in astronomy can be found in the logarithmic nature of the eye as a sensor as well.

Yes, good point. Perception of some things has logarithmic response. Within in certain ranges, of course.

It's funny because I first imagined the seeing/hearing comment as pitch & color, rather than volume & brightness. Pitch certainly feels somehow naturally logarithmic. But we can hear linear differences as easily as we can hear logarithmic differences. Within certain ranges, of course.

> Within certain ranges, of course.

Citation needed. I've never heard of human senses being anything else than logarithmic.

Sure, here you go. I said "within certain ranges" because there are absolute limits on either end. I hope it's obvious to you that the logarithmic approximation is only logarithmic until it isn't. The human visual response to staring at the midnight sky and staring at the noon sun are both non-logarithmic relative to the well lit everyday objects you usually look at. The valid range does not extend infinitely in either direction, and at the ends response ceases to be logarithmic even if the middle of the range works out well.

So, I think no citations are needed to explain basic absolute limits and the simple fact that logarithmic perception is only valid "within certain ranges." But, since you asked for citations, here are some starting points for understanding lightness perception, and how it's not quite logarithmic even in the middle of the valid range.

http://www.telescope-optics.net/eye_intensity_response.htm

"All this only scratches the surface of the complexities of eye response to light intensity, but should illustrate well that the common notion of it being described as simply logarithmic is oversimplification, to say the least."

https://en.wikipedia.org/wiki/Lightness

"At first glance, you might approximate the lightness function by a cube root, an approximation that is found in much of the technical literature. However, the linear segment near black is significant, and so the 116 and 16 coefficients. The best-fit pure power function has an exponent of about 0.42, far from 1/3."

https://en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law#Visi...

"The eye senses brightness approximately logarithmically over a moderate range (but more like a power law over a wider range)"

https://en.wikipedia.org/wiki/Absolute_threshold

"For white light, the absolute sensitivity found was 5.9 x 10−14 watts / steradian-cm2"

https://en.wikipedia.org/wiki/Orders_of_magnitude_(luminance...

"100 Mcd/m2 Possible retinal damage[1]"

https://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot...

see page 276, Fig. 16.2 "Approximate ranges of of vision regimes"

http://retina.anatomy.upenn.edu/~rob/lance/units_photometric...

See "Light levels important to vision"

Log scales actually are intuitive to humans. As thinking about things relative to each other is much simplier when they are not easily quantized.

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