What is a logarithmic scale? Why is it more useful for some things than a regular numerical scale?
In: Mathematics
Imagine you wanted to plot the net worth of people in your area in a graph that shows all the data.
Now most of the net worth will be around the lower end with some higher in between. So you can nicely see how the worth is distributed among the people.
Then suddenly Elon Musk decides to join your area. Now your nice graph is screwed.
Why is it screwed? Because the number line that previously was at let’s say 500k max suddenly jumped to 147 billion.
So the graph, as it is supposed to show all points, now is squished such that Elon Musk is at the top, a single outlier in the whole distribution. Even the richest guy in your area before is a measly 0.00034% on the scale. (Yes that’s right, those are 3 zeros after the decimal AND it’s percent. That is how laughable 500k are in that distribution)
This makes it impossible to see any difference between the 500k guy and the 300k guy the 30k guy and so on. They’re all down in the same line from Elons perspective.
So now you take a logarithmic scale, meaning you take their net worth, throw it into a logarithmic function and then plot that value. You obviously have to adjust the y axis accordingly.
The 30k guy is now a 4.47.
The 200k guy is now a 5.3.
The 500k guy is now a 5.7.
And Elon? Well he’s an 11.17.
These now fit on a single graph and you can still make out differences between the “smaller” numbers.
Logarithmic scales are generally often used when exponential growth is concerned, like population growth, spreading of diseases. Also when you have to work with data that spans a huge range of values, like comparing the size of objects in the universe.
Using logarithmic scales and transformations is very common in machine learning and data science.
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