A number the graphs showing the growth of the virus may seem a bit puzzling. As you’ll see, the thing to look carefully at is the left (vertical) axis. The bottom (horizontal) one is usually time; days, hours, weeks etc and pretty straightforward.
So, consider this simple – and delicious – example. Case 1. Something is growing by adding 2 every day. Say, I give you 2 chocolates every day. Here’s the number or chocolates you have after each day:
A quick graph in Excel – your total number of chocolates versus time (in days) – is a straight line also known as linear:
So now Case 2. What if once a week you give 10 people a single chocolate.
Then a week later, each of those 10 people give 10 other people a single chocolate.
I’ve done that in Excel. Ignore the individual Days (they are used for the graph) and focus on the blue-highlighted rows; each week (7 days):
Phew. It’s growing madly. You may have seem something like this before; the classic ‘breeding like rabbits’ example. Or, for us recently, viral infections, but (only!) if left unchecked.
Let’s graph Case 2. It climbs slowly and then…just takes off. This is called exponential growth.
It’s actually hard to show such a huge range of data/chocolates – from 10 to 1,000 to 26,000 – clearly on the one graph. As you can see, you really can’t make out the 1000-sized values, let alone the 10.
Logs to the rescue
Maths time. Nothing more than high school level, so hang in there. It’s all about Powers of Ten: 10 raised to the 1st power is 10, to the 2nd is 100 and so on:
The green numbers are of interest here. The reverse way of looking at it is: what number do I raise the 10 to, in order to get (say) 100? The answer is 2.
You may remember this 2 as being the logarithm of 100. (Officially we’d need to say ‘base 10 logarithm’ but we won’t)
Here’s how that’s written, log being the abbreviation of logarithm:
See my clever use of colour? 🙂
Graph the Log?
Yes, let’s try that. Firstly we’ll get Excel to calculate the Log of those big numbers in Case 2. Again ignore the single day, figures and focus on the blue/weekly ones:
Interesting. They don’t go galloping off wildly. So what does the graph look like? Speaking of interesting:
Linear!? Not really. It is actually showing the same data as the big curve (above), but how we show it is different. We are showing the curve as a ‘straight line’, via using the Log.
Two very important comments:
- I’m not trying to show the exact virus curves/lines per se, for us or any country. They are more complex. I’m just trying to explain what a Log graph is as some of the virus charts use Logs.
- Despite what it may seem, re-drawing the Curve as a Line (via the Log) is not flattening the curve. That’s different and explained here.
To finish up, I’ll re-do the above Log chart with some extra explanations added in:
Ok, the main message is to look at that left side on any chart you see. It may just show values like 10, 100, 1000, 10000. That’s a huge clue it’s a Log graph. They make it easier to see the small (10), medium (100) and large (10,000) numbers on the one chart. The bottom scale is really linear; just days evenly spread out.
As I said, the actual viral graphs won’t be a straight line, but the focus here is understanding the scale used to show the data. Linear or Log.
True story: when I was doing 4th Year Physics at Monash, the running joke was: if the graph from your experiment's results wasn't showing the values the theory predicted, then just re-do with it a Log scale, because they're always a straight line :-)