# Ambiguous sums just don't add up

04-Aug-2010

A colleague recently bought one of those new-fangled iPad machines. He's been having fun installing app after app, including a 3rd party calculator app called Calcbot.

I'm not writing this blog post to point out how absurd it is that us modern geeks spend hundreds of pounds on shiny new gadgets, then end up using them as replacements for our perfectly capable Casio calculators from the 80's. Nor am I writing to complain that the iPad calculator can't do one of the most basic (and fun) tasks our £10 Casios could handle - typing in "5318008" then turning the calculator upside down. Try this on an iPad and it'll auto-rotate the screen, denying future generations of school kids the chance to sit there sniggering at the back of afternoon maths class (damned those accelerometers!).

No, the reason I'm writing is that Calcbot (and its ilk) don't even add up correctly!

To be specific - my colleague complained that when he typed 100 + 25% into Calcbot he got the answer 100.25. What's wrong with that I asked? Turns out he was expecting 125. But that's not right - in the original sum the 25% doesn't relate to anything - it's just sitting out there on its lonesome, ready to be added to whatever happens to be to the left of the plus sign. As we all know, 25% can also be written as 0.25, so the original sum could also be represented as 100 + 0.25. Calcbot's answer of 100.25 seemed perfectly reasonably to me.

Of course, I understand why my colleague was expecting 125. What he meant was "100 + 25% of 100". However, to represent this mathematically you should type 100 * 1.25, or 100 + (100 * 0.25) if you like. 100 + 25% is ambiguous at best.

At this point you might be thinking, "Hang on MrCeri, I thought you said Calcbot can't add up, yet here you are defending it - where's the beef!?"

Good question. Beef indeed. Here's the beef - a number of (innumerate) users complained about Calcbot, bemoaning the fact they could no longer work out their percentages like they used to. So what did the developers of Calcbot do? They broke maths in order to make their app work for the iPad community.

I contacted Calcbot to ask why they gave in, why they broke their perfectly functional adding machine just to please the twittering masses - why, indeed, did they break maths itself? Their answer? "Try it in the Apple calculator, that's the way it's always worked." And do you know what? They were right. I tried the offending sum in a few apps, and here's what you get:

Apple calculator: 125
Vista calculator: 125
Excel: 10025.00%

I contacted Calcbot again, reminding them of one of the basic rules of algebra:

a + b = b + a

So 100 + 25% should give the same result as 25% + 100. They didn't reply this time. I can only assume they're too busy weeping to the great Casio Gods in the sky.

Now, in all seriousness, and in fairness to Calcbot, I understand perfectly why they changed their app to make it consistent with the default Apple (and indeed Microsoft) calculator. Calcbot aren't the baddies here. What saddens me is that users were complaining in the first place, that the general population doesn't even have enough of a grasp of basic maths to understand why 100 + 25% doesn't (necessarily) equal 125.

Somewhere, maths is weeping. I imagine it looks a bit like this:

Poor maths.