3. A Troublesome Tweet

I come from a very sporty family and anything that involves chasing after a ball generally catches my interest. I couldn’t avoid reading about the following tweet from cricketer Stuart Broad (the England fast bowler) that made a stir in the news recently.

Stuart Broad, England Fast Bowler

"I've heard if you earn minimum wage in England you're in the top 10% earners in the World. #Keep Humble”

The backlash caused by this tweet resulted in Broad having to issue a rather grovelling apology. 

Now setting aside for the moment the tactfulness of how he worded his tweet, was his claim actually true? There are two parts to this – the earnings of someone on the minimum wage and the pattern of all earners, globally. 

Minimum Wage Earnings: A quick scan in Google revealed that the national minimum hourly rate for UK adults, at the time of writing, is £6.50. Working, say, a 40 hour week, this gives a weekly wage £260 or roughly £13,500 annually. (Assume a 37 hour week and this figure drops to £12,500 annually.)

Global Earnings: A harder task was to get a picture of world earnings. Again, with the help of Google, I was able to find a Daily Mail article which provided some useful tidbits of information – for example:

* You need to be earning just £22,000 per annum to be in the world’s top 1% of earners.

* Half of the world’s richest 1% live in the USA.

Now this is all interesting stuff, but it didn’t quite resolve whether Stuart Broad’s claim was true. Some further googling turned up what I was looking for – an on-line calculator called the Global Rich list, posted by the charity, Care International. You simply enter a figure for your annual earnings and it tells you where you fall within the global rich list. 

First, I tried entering the earnings of a UK pensioner receiving the full state pension, which is currently £113.10 per week – i.e. roughly £5880 per year. Using the online calculator, this puts a British pensioner into the top 18% of earners, globally.

Next, I entered the earnings of someone on a minimum wage – £13 500 annually. 

The on-line calculator put this earner into the top 5.41% of earners, globally – a figure even smaller than the 10% claimed by Stuart Broad. 

So these calculations do seem to bear out Stuart Broad’s claim with something to spare. I wondered afterwards why making what appears to be a factually correct statement could cause such a furore. A likely explanation is how Broad presented it – you may have noticed that he had tacked onto the end of his tweet the words: #Keep Humble. He claimed afterwards that this hashtag was aimed at himself. But for someone who reputedly earns upwards of £1million per year, he is open to the accusation of lecturing at those earning a tiny fraction of what he earns by telling them how lucky they are!

Finally, here's what the lightbulb team are getting up to.

Postscript

I wondered whether these figures from the Global Earnings calculator were to be believed? When it comes to statistical claims, it’s always sensible to look for loopholes and alternative explanations. I consider some of these here in my website, MathinPictures.co.uk, along with the sources I used.

2. The rat, the pallet and the logs

The rat: The recent cold snap has encouraged Sheila and myself to be more enthusiastic about putting seeds and nuts on the bird table. But in recent weeks, an uninvited guest has joined the party. Yes, Mr. Rat has been busy helping himself as well. Last week, I had my camera at the ready and here’s the moment when he realised he was rumbled. 

Rumbled

In a flash he was off, making a rapid leap for freedom, disappearing around the side of the house.

The leap for freedom

‘I bet your life he’s living under that tarpaulin where we store the logs,’ Sheila said straightaway and I rather felt that she was right. We removed the tarpaulin and carefully started reorganising the logs. But all we uncovered was a very sleepy, plump frog. 

We could see that the logs at the bottom of the pile had started to rot and gather moss. What we needed was a large pallet to go underneath, but where would we get one of those?

The pallet: Two days later, I was driving into town to pick Sheila up from a little light shopping. The footpaths were jammed with pedestrians and the roads were busy with commercial vehicles trying to unload goods. As I approached our usual pick-up point, I could see that there was a bit of a commotion. It seemed that the footpath was blocked – mothers with prams and pushchairs were having to step into the road to get past. It was then that I spotted the source of the blockage, waving at me frantically. There she was, making her way slowly along, staggering under the weight of the largest pallet I have ever seen – it looked like it weighed a ton. It turned out that she had found it at the back of a local TV store (what was she doing there?).

With difficulty we managed to get it into the car and home. It now forms the base of our new log store. So I just need to send Sheila out to liberate a few more pallets of a similar size and shape and our log store will be complete.

Logs: While we were working on the wood pile, I asked Sheila what she remembered of logarithms at school.  She laughed. “I remember a book with big numbers in. I don’t know what we did with them though.”

The book of mystery from schooldays

So, what does the average person understand by the word logarithm – a term I’ve worked with all my life? I emailed a few of my friends and they all graced me with interesting and entertaining responses, from which here's a selection.

* Umm, log tables, looking things up that didn't make sense, then I had an exotic looking calculator and I still have no idea. (age 44)

* I know that a logarithm is something to do with sums, and that there are log tables, but I can’t help you any further. I have to say that I would have expected you to know what a logarithm is without having to ask. (age 65)

* Absolutely no idea whatsoever. (age 42)

* Something from school days -– slim book with columns of very long numbers in. Some kind of crazy multiplication? (age 67)

* I cannot think of any other bit of schooling where the books on the memory shelves have snapped so firmly shut. (age 62)

* Without looking it up I wouldn’t know the word logarithm, other than thinking it is a mathematical equation of some sort. (age 31)

One reply was a perfect textbook definition and it came from my neighbour Andy: 

* It's the power to which the base number is raised to get the number in question.

Have a gold star Andy and go to the top of the class! 

So, overall, the little book and its columns of numbers was well remembered by most of the over sixties age group, but very little else of any substance!

What IS a logarithm?: Although Andy's definition is correct, it may be too dense for most people to grasp at a single reading. Learning about logarithms needs a little patience. If you're interested in knowing what a logarithm is, I've made a short YouTube video which you can view here.

But a trickier question is, what’s the point of logarithms and why do we need them. Relax – I won’t explain that now but I hope to return to it in a future post. Instead, here's another 'lightbulb' joke.

Postscript

If you are interested in finding out more about logarithms and their properties, have a look here in my website, MathinPictures.co.uk.

1. Twice as warm

Our son, who is an actor has just come back from a 3-month tour and this week he moved into a new flat in south London. So, very early last Sunday, Sheila and I filled the car with possessions that he had been storing in our spare bedroom and set off for London to help him move them in.

The first thing we noticed on stepping out of the car was the temperature in London that morning – decidedly brisk. Leo was waiting to greet us outside the modern, red-bricked, 6-storey apartment block. ‘Top floor, Leo’ I asked, joking. ‘That’s right.’ Leo replied, but unfortunately he wasn’t joking!

Returning to the Midlands that afternoon Sheila remarked, 'It's twice as warm here as it is in London!' But is it really possible for one temperature to be twice as warm as another? We keep a thermometer in the garden. It is marked in Celsius down the left side and Fahrenheit down the right and the reading was 10ºC. 

The garden thermometer

I googled the weather details for that day and the temperature in London had been 5ºC. 

So Sheila was pretty pleased to hear this information. 
'Just as I said – twice as warm here as in London!'

But temperature is one of those funny measures where it doesn't make sense to talk about 'twice as warm', 'four times as warm' and so on. The evidence is revealed when you shift to a different unit of measure – say to the Fahrenheit scale. We looked closely at the two scales side by side. 

Celsius on the left, Fahrenheit on the right

When using the Celsius scale on the left, 10º was twice 5º. But coming across to Fahrenheit, the two corresponding temperatures were 50ºF and, roughly, 40ºF. Clearly these two readings did not share the same pattern: 50 is not twice 40.

Anyway, that's measurement for you. I'll end this post on a 'light' note with this little rib-tickler.

Postscript

So, when comparing two temperatures there's no such thing as 'twice as warm'. The same issue crops up when talking about time of day – you can't sensibly talk about 'twice as late'. But you can talk about 'twice as far', 'twice as heavy', twice as many', etc.
If you are interested in finding out more about measuring scales and their properties, you’ll find an explanation here in my website, MathinPictures.co.uk.