3 ms·

Log scales are extremely misleading. It looks like computing power has only increased a bit since the 1980s, when in fact it has increased orders of magnitude.

Log scales are extremely misleading. It looks like computing power has only increased a bit since the 1980s, when in fact it has increased orders of magnitude. Especially for a general audience, but even people familiar with log scales, it doesn't give an intuitive feel of the actual numbers.

jacobolus 11y ago
I agree with you that not enough people are familiar with log-scale charts, but that’s a problem with experience, not with “intuition”. Log-scaled charts give perfectly fine “intuitive feeling” for anyone who is used to reading them. Which would include most people if log-scaled charts were more ubiquitous. I am lamenting that they are not, because for many, many purposes they are easier to read and facilitate more useful intra-chart comparisons than linear-scaled charts. In particular, they make the slope of lines meaningful in many cases where linear-scaled charts do not. They also fit much more useful information about relative magnitude and allow us to read a couple significant digits of numbers across a wide range of scales. Any time there is more than 2 orders of magnitude difference among values a chart, a linear scale becomes nearly useless. Reading charts at all is an acquired skill, and takes a lot more practice than you might expect. Just like doing arithmetic with fractions, decimals, or angles of a circle is an acquired skill, or driving a car is an acquired skill. If you study young children or people from non-literate cultures, you’ll see all kinds of difficulty reading linear-scaled charts. Edit: here, I spent a couple minutes making a linear-scaled and a log-scaled chart of the wikipedia $/gigaflops table from elsewhere in this thread, using Matlab. See how much useful information you can get from the linear-scaled chart: http://i.imgur.com/A80Tr6V.png http://i.imgur.com/A80Tr6V.png http://i.imgur.com/xG0mngX.png http://i.imgur.com/xG0mngX.png (On the log-scaled chart, if we penciled in a grid, you could get at least one significant figure out of each data point, despite the data spanning 11 orders of magnitude. On the linear-scaled chart, you get 2 significant figures for a single data point, but there’s no way to make any distinction at all between the rest of the values, which span about 8 orders of magnitude.)
- Houshalter 11y ago
  IMO neither chart gives an intuitive feel for the data. That nice straight line does nothing to emphasize just how rapidly the price dropped over the last 10 years. That's why I listed a table of the raw numbers instead of a graph. People understand the scale of numbers, and the scale isn't lost by trying to cram it into a chart. The video used a zooming chart, which solves both problems.
  - jacobolus 11y ago
    > That nice straight line does nothing to emphasize just how rapidly the price dropped over the last 10 years Sure it does. The number goes from 10^12 down to 10^-1, 13 orders of magnitude. You can easily read these off the side or count the number of grid lines crossed. (Whoops, I wrote 11 in my comment before.) If you’re used to reading a log-scaled chart, counting the powers of ten along the vertical axis is perfectly “intuitive”, or at any rate just as “intuitive” as any other way you could write these. In distance scale terms, this is the same as going from nanometers to tens of kilometers. Or in time scale terms from milliseconds to hundreds of years. Numbers with such a big difference in scale are to some extent inherently incomparable: We don’t interact with such a range of scale with most of our naked senses, but need tools to understand and compare such divergent numbers. (Though if you’re hunting for an analogy, comparing volume or mass might be slightly easier, as they scale with length cubed. 13 orders of magnitude gets you from the mass of a human egg cell up to the mass of a tank.)
  - aninhumer 11y ago
    A list of numbers also functions as a slightly messy ascii log graph.

jacobolus 11y ago

I agree with you that not enough people are familiar with log-scale charts, but that’s a problem with experience, not with “intuition”. Log-scaled charts give perfectly fine “intuitive feeling” for anyone who is used to reading them. Which would include most people if log-scaled charts were more ubiquitous. I am lamenting that they are not, because for many, many purposes they are easier to read and facilitate more useful intra-chart comparisons than linear-scaled charts. In particular, they make the slope of lines meaningful in many cases where linear-scaled charts do not. They also fit much more useful information about relative magnitude and allow us to read a couple significant digits of numbers across a wide range of scales. Any time there is more than 2 orders of magnitude difference among values a chart, a linear scale becomes nearly useless. Reading charts at all is an acquired skill, and takes a lot more practice than you might expect. Just like doing arithmetic with fractions, decimals, or angles of a circle is an acquired skill, or driving a car is an acquired skill. If you study young children or people from non-literate cultures, you’ll see all kinds of difficulty reading linear-scaled charts. Edit: here, I spent a couple minutes making a linear-scaled and a log-scaled chart of the wikipedia $/gigaflops table from elsewhere in this thread, using Matlab. See how much useful information you can get from the linear-scaled chart: http://i.imgur.com/A80Tr6V.png http://i.imgur.com/A80Tr6V.png http://i.imgur.com/xG0mngX.png http://i.imgur.com/xG0mngX.png (On the log-scaled chart, if we penciled in a grid, you could get at least one significant figure out of each data point, despite the data spanning 11 orders of magnitude. On the linear-scaled chart, you get 2 significant figures for a single data point, but there’s no way to make any distinction at all between the rest of the values, which span about 8 orders of magnitude.)

Houshalter 11y ago
IMO neither chart gives an intuitive feel for the data. That nice straight line does nothing to emphasize just how rapidly the price dropped over the last 10 years. That's why I listed a table of the raw numbers instead of a graph. People understand the scale of numbers, and the scale isn't lost by trying to cram it into a chart. The video used a zooming chart, which solves both problems.
- jacobolus 11y ago
  > That nice straight line does nothing to emphasize just how rapidly the price dropped over the last 10 years Sure it does. The number goes from 10^12 down to 10^-1, 13 orders of magnitude. You can easily read these off the side or count the number of grid lines crossed. (Whoops, I wrote 11 in my comment before.) If you’re used to reading a log-scaled chart, counting the powers of ten along the vertical axis is perfectly “intuitive”, or at any rate just as “intuitive” as any other way you could write these. In distance scale terms, this is the same as going from nanometers to tens of kilometers. Or in time scale terms from milliseconds to hundreds of years. Numbers with such a big difference in scale are to some extent inherently incomparable: We don’t interact with such a range of scale with most of our naked senses, but need tools to understand and compare such divergent numbers. (Though if you’re hunting for an analogy, comparing volume or mass might be slightly easier, as they scale with length cubed. 13 orders of magnitude gets you from the mass of a human egg cell up to the mass of a tank.)
- aninhumer 11y ago
  A list of numbers also functions as a slightly messy ascii log graph.