5 ms·

Why not rather think about wealth on a log scale ?

sushisource 9y ago
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.
- welterde 9y ago
  One would think it would be since we hear and see in log scale.
  - zild3d 9y ago
    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
    - welterde 9y ago
      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.
      - majewsky 9y ago
        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.
  - dahart 9y ago
    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.
    - welterde 9y ago
      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.
      - dahart 9y ago
        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.
        majewsky 9y ago
        > Within certain ranges, of course. Citation needed. I've never heard of human senses being anything else than logarithmic.
        dahart 9y ago
        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 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 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#Vision 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 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)#cite_note-lance-1 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-org/Sample-Chapter.pdf 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.html http://retina.anatomy.upenn.edu/~rob/lance/units_photometric... See "Light levels important to vision"
  - deleted 9y ago
    [deleted]
- undersuit 9y ago
  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?
- kemerover 9y ago
  Log scales actually are intuitive to humans. As thinking about things relative to each other is much simplier when they are not easily quantized.
wolf550e 9y ago
Many people cannot visualize log scale.
- ttoinou 9y ago
  Well that's what visualization are for. Wealth might be more "multiplicative" than "additive", hence a log scale would be more suitable to study it
deleted 9y ago
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dahart 9y ago
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.
- ttoinou 9y ago
  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
  - dahart 9y ago
    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.

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.

welterde 9y ago
One would think it would be since we hear and see in log scale.
- zild3d 9y ago
  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
  - welterde 9y ago
    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.
    - majewsky 9y ago
      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.
- dahart 9y ago
  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.
  - welterde 9y ago
    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.
    - dahart 9y ago
      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.
      - majewsky 9y ago
        > Within certain ranges, of course. Citation needed. I've never heard of human senses being anything else than logarithmic.
        dahart 9y ago
        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 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 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#Vision 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 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)#cite_note-lance-1 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-org/Sample-Chapter.pdf 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.html http://retina.anatomy.upenn.edu/~rob/lance/units_photometric... See "Light levels important to vision"
- deleted 9y ago
  [deleted]
undersuit 9y ago
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?
kemerover 9y ago
Log scales actually are intuitive to humans. As thinking about things relative to each other is much simplier when they are not easily quantized.

wolf550e 9y ago

Many people cannot visualize log scale.

ttoinou 9y ago
Well that's what visualization are for. Wealth might be more "multiplicative" than "additive", hence a log scale would be more suitable to study it

deleted 9y ago

[deleted]

dahart 9y ago

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.

ttoinou 9y ago
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
- dahart 9y ago
  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.