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
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.
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.
"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."
"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."
If your goal is to be able to plot incomes of a wide variety of people and be able to visually see the difference between poor and average as well as you can see the difference between average and super-rich, then a log scale is the way to do it.
The goal of the comment you replied to, however, is to demonstrate the vastness that orders of magnitude have. It's to compare average people to super-rich, and get a stronger intuitive sense of how much wealthier a billionaire is than the average person, and how much wealthier Bezos is than the average billionaire. Using a log scale doesn't help that goal at all, a log scale actively compresses the range and prevents intuitive physical comparisons & analogies.
But a log scale is interesting because when you switch of scale, you change the meaning of money.
1) First stages of the visualization would show people from country where the money measure doesn't mean anything at all
2) Then powers of ten later it show how disparately "rich" people are in countries where this measure has a little more significance
3) Powers of tens later you see big companies and rich billionnaires like in this article == Money Is Power (Jeff Bezos is not going to buy one billion baguette de pain tomorrow I can assure you that)
4) Then of course you see higher in the scale huge aggregate of macro economics stuff which no one really have control over or understands
Log scales are interesting for lots of reasons, and they are incredibly useful. Everyone here knows that, and nobody disagrees. But you asked why not think about log scale in response to someone who was attempting to demonstrate absolute differences. Log scales are for showing ratios, they are not for showing absolute differences.
The point here isn't to say that Bezos will buy a billion baguettes, but it is show to show that he could buy 90 billion baguettes and feed every single person on the planet several times over. There are only a few people who could do this. And, of course, they won't.
EDIT: I meant simply that 90B baguettes would go as far as they go, and 90B baguettes is several times more than 7B people. I was only demonstrating magnitudes in the context of a thread about magnitudes. I am not suggesting that either baguettes or Bezos are a permanent and global solution to world hunger & politics, but either way I can't afford to buy very many people baguettes.
> The point here isn't to say that Bezos will buy a billion baguettes, but it is show to show that he could buy 90 billion baguettes and feed every single person on the planet several times over. There are only a few people who could do this. And, of course, they won't.
Because, even if they did, buying baguettes won't fees the hungry; acquiring food isn't the hard/expensive part, distributing it is. And it's not hard in a “We know how to make it work but have insufficient funds dedicated” way, but in a “we don't know how to do it effectively at any cost” way.
Even if Bezos wanted to feed every person on the planet, how exactly would he be able to do that?? People are controlled by governments, and governments are highly corrupt. They'd probably keep all the baguettes for themselves.
I agree with the first part of the comment, but then if you really think the second part of your comment is true, then I was right to make my comment.
Jeff Bezos CANNOT solve world issues like this (food crisis for our example). This is so silly I don't know even where to start. Theses issues were not solved in our countries thanks to the Jeff Bezos of 1817... What makes you think that giving 1 / 10 / 100 billion dollars would feed Africa for example ? Describe to me all the steps I'm very interested
It seems like you misunderstood my comment and started arguing your own straw man issue. I'm going to pass on that one and stick to the point: using linear scales is more useful for physical analogies and cartograms than log scales. I like log scales, and I, like you, think it's really useful to evaluate rich people and global finances on a log scale in addition to appreciating the magnitudes by thinking about them linearly and using physical analogies. I don't think there's any good way to say what @kens' said using a log scale. So if you agree and acknowledge that linear scales and log scales are both useful, then we agree. If you disagree that linear scales are useful or should ever be used, but you are genuinely still asking why, then I can try to help. If you disagree that linear scales are useful and you don't want to hear about why, maybe we should stop arguing?
