3 ms·

Log scales are impossible to reason about unless you're dealing with exponential data. Otherwise, the transform is meaningless because log is literally an expon

by rcme 4y ago

Log scales are impossible to reason about unless you're dealing with exponential data. Otherwise, the transform is meaningless because log is literally an exponent, so not having an exponent in the data is equivalent to garbage in, garbage out, more or less.

nerdponx 4y ago
The quote literally explains how to reason about it.
- rcme 4y ago
  > "doubled" is the same distance from "stayed the same" as is "halved." What's more natural: looking at a change relative to 0, or looking at a change relative to all the other points? Personally, I think looking at a change relative to 0 makes much more sense. Trying to figure out the meaning of the points by looking at relative values is garbage, because there is no underlying exponent to justify the use of the logarithm.
  - rssoconnor 4y ago
    If the number of students enrolled in my course goes up by 25% one year, and then the next year the number of students enrolled in my course drops by 20%, how many students are now in enrolled in my course compared to the beginning? What if it were reversed: what if the number of students dropped by 20% one year, and then when up by 25% the following year. How many students are now enrolled in my course compared to the beginning in this scenario?
    - rcme 4y ago
      In any scenario like that, where a quantity X changes by Y% and then that new quantity changes by Z%, I almost always think about it like (1 + Z) * ((1 + Y) * X). That is, I compute the new size after adjusting by Y% first, and then take Z% of that. To me, this is still treating values as magnitudes from 0 and the Y% change is totally independent from the Z% change. I guess you can multiply Y and Z first, but that’s not how I think about it.
      - jonahx 4y ago
        rssoconner is saying that answering those questions becomes trivial when using the log scale. I find this argument persuasive despite having the same reaction you did to the original graph. The rewritten version is easier to understand immediately and is less confusing, but it's not as usable for answering questions about the data. If the original author's had included a brief explanation of the unexpected looking axis label and its advantages, the whole problem would have been avoided. And I think the argument that "log scales are standard" is not a valid defense here, as this whole thread demonstrates.
      - rssoconnor 4y ago
        Point is that it seems by the above calculation that a change of increase-by-25% and a change of decrease-by-20% are opposite changes of equivalent magnitude as they perfectly cancel each other out. This is why they are plotted equidistant from 0% on the original chart.
kurthr 4y ago
I think there is a world of electrical and acoustic engineers that would beg to differ. The dB scale is very common, useful, and easy to understand over a large range of amplitudes for very linear systems. Resonance plots are an example where data is unreadable without and easily readable with log plotting. Wide ranges of delta% (from unity=100%) seem like another good choice.
- rcme 4y ago
  The change you experience in a sensation is related to how much you're already sensing that thing. This applies to hearing and vision and is known as Weber–Fechner law: https://en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law https://en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law What this means in practice is that human senses are a logarithm of the input. Because hearing is a logarithm of the input, we deal with the perception of sound in exponential quantities of sound.
  - lathyrus_long 4y ago
    Log scales are also widely used for physical quantities that humans can't directly perceive, like radio-frequency electric fields. The logarithmic nature of human perception provides an additional benefit in some cases, but it's not the sole or primary benefit. For example, the amplitude response of any linear differential equation to a sinusoidally varying input is (roughly, at low Q, etc.) piecewise linear vs. frequency on a log-log Bode plot. It has no similarly useful structure on a linear plot. That structure is relevant to all manner of problems in electromagnetics, optics, acoustics, dynamics in mechanics, and other areas. Any introductory course in signals and systems will cover it. That's not very relevant to this university chart, though. For a simpler example, stock price charts are sometimes logarithmic. On such a chart, if I buy a constant dollar amount and then sell it, I'll make the same dollar gain or loss for any buy and sell points the same vertical distance apart. I believe this chart's creator was thinking of an analogous property; the labels are placed in pairs geometrically equidistant from 0%, since (1 + 0.25)*(1 - 0.2) = (1 + 0.5)*(1 - 0.333...) = 1. I believe the rounding to 34% and not 33% is a mistake, but that the scale is otherwise fine.

by rcme 4y ago

nerdponx 4y ago

The quote literally explains how to reason about it.

rcme 4y ago
> "doubled" is the same distance from "stayed the same" as is "halved." What's more natural: looking at a change relative to 0, or looking at a change relative to all the other points? Personally, I think looking at a change relative to 0 makes much more sense. Trying to figure out the meaning of the points by looking at relative values is garbage, because there is no underlying exponent to justify the use of the logarithm.
- rssoconnor 4y ago
  If the number of students enrolled in my course goes up by 25% one year, and then the next year the number of students enrolled in my course drops by 20%, how many students are now in enrolled in my course compared to the beginning? What if it were reversed: what if the number of students dropped by 20% one year, and then when up by 25% the following year. How many students are now enrolled in my course compared to the beginning in this scenario?
  - rcme 4y ago
    In any scenario like that, where a quantity X changes by Y% and then that new quantity changes by Z%, I almost always think about it like (1 + Z) * ((1 + Y) * X). That is, I compute the new size after adjusting by Y% first, and then take Z% of that. To me, this is still treating values as magnitudes from 0 and the Y% change is totally independent from the Z% change. I guess you can multiply Y and Z first, but that’s not how I think about it.
    - jonahx 4y ago
      rssoconner is saying that answering those questions becomes trivial when using the log scale. I find this argument persuasive despite having the same reaction you did to the original graph. The rewritten version is easier to understand immediately and is less confusing, but it's not as usable for answering questions about the data. If the original author's had included a brief explanation of the unexpected looking axis label and its advantages, the whole problem would have been avoided. And I think the argument that "log scales are standard" is not a valid defense here, as this whole thread demonstrates.
    - rssoconnor 4y ago
      Point is that it seems by the above calculation that a change of increase-by-25% and a change of decrease-by-20% are opposite changes of equivalent magnitude as they perfectly cancel each other out. This is why they are plotted equidistant from 0% on the original chart.

kurthr 4y ago

I think there is a world of electrical and acoustic engineers that would beg to differ. The dB scale is very common, useful, and easy to understand over a large range of amplitudes for very linear systems. Resonance plots are an example where data is unreadable without and easily readable with log plotting. Wide ranges of delta% (from unity=100%) seem like another good choice.

rcme 4y ago
The change you experience in a sensation is related to how much you're already sensing that thing. This applies to hearing and vision and is known as Weber–Fechner law: https://en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law https://en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law What this means in practice is that human senses are a logarithm of the input. Because hearing is a logarithm of the input, we deal with the perception of sound in exponential quantities of sound.
- lathyrus_long 4y ago
  Log scales are also widely used for physical quantities that humans can't directly perceive, like radio-frequency electric fields. The logarithmic nature of human perception provides an additional benefit in some cases, but it's not the sole or primary benefit. For example, the amplitude response of any linear differential equation to a sinusoidally varying input is (roughly, at low Q, etc.) piecewise linear vs. frequency on a log-log Bode plot. It has no similarly useful structure on a linear plot. That structure is relevant to all manner of problems in electromagnetics, optics, acoustics, dynamics in mechanics, and other areas. Any introductory course in signals and systems will cover it. That's not very relevant to this university chart, though. For a simpler example, stock price charts are sometimes logarithmic. On such a chart, if I buy a constant dollar amount and then sell it, I'll make the same dollar gain or loss for any buy and sell points the same vertical distance apart. I believe this chart's creator was thinking of an analogous property; the labels are placed in pairs geometrically equidistant from 0%, since (1 + 0.25)*(1 - 0.2) = (1 + 0.5)*(1 - 0.333...) = 1. I believe the rounding to 34% and not 33% is a mistake, but that the scale is otherwise fine.