Maths Homework

I've decided that smartphones and their apps have finally meant the proper 21st Century has arrived. The fact that the technology has grown organically rather than exploded in a sudden burst of flying cars and "beaming up" doesn't make it any less powerful or significant - we are living in an amazing space age where the impossible has crept up on us. Who could have imagined, even just 5 years ago, that you could pull a phone out of your pocket and visually drive down any road in the World? Hold it up to the sky and see every star and planet or merely every commercial aircraft? Look up, order or sell anything to anyone? We ARE the Jetsons.

When I was at school we multiplied two numbers together by looking up their logarithmic powers in a mass of tables, adding them together then reversing the look-up to find the product. Or we did the equivalent with a ruler with a central sliding section which was accurate to about 10%. If we wanted to travel any distance, we'd pull out tattered Esso Maps and trace the possible routes with our fingers across different pages to find a suitable path - now we just pop in a Postcode to our "device" and 18 geostationery satellites send unique beams to our device which then wondrously calculates from the time delays our exact position against a digital grid. It's blinking marvellous!

But even GPS technology has a weakness. Since the satellites were reprogrammed to remove a randomized error about 10 years ago (after worry about foreign military use had subsided) they have been able to track us to within a few feet. However, they still mainly rely on Postcodes, which often give a very general idea of a location particularly in Country areas where house numbers are sparse - witness the number of delivery drivers in our road desperately looking for a particuular house name. They could be pinpointed exactly with digital map coordinates, but who in their right mind wants to remember 14 digital numbers?

Now a young business start-up in London has come up with a brilliant solution. They are called  "What 3 Words", and they have divided the entire Earth's surface into individual 3m x 3m squares and given each one a unique identifier in the form of three words - just three words to pinpoint any precise point anywhere in the World. Any one of us can get to remember a string of three words easily enough, certainly a lot easier than coordinates or even postcodes.

But I started wondering just how they could possibly have enough words to cover such a vast area. Surely the area is so great, particularly including Oceans (which make up 70% of the World's surface) that there aren't enough unique words in the largest dictionery. At first I wondered if they were incorporating foreign languages as well as English, but thay claim to do it all with English words.

Let's do the maths. (Or "Math" if you an American citizen or cartoon character).

The surface area of the Globe is 510,072,000 square kilometres.

1 square kilometre = 1000*1000 = 1,000,000 square metres

Each target square is 3mtr x 3mtr = 9 square metres

So every square kilometre of the Earth contains 1,000,000 divided by 9 = 111,111 target squares.

Therefore the number of target squares in the whole earth = 510 million x 111,111 = 56,666,610 million, or 56,666,610,000,000 squares

I believe that is in English nearly 57 TRILLION squares.

(Stop talking at the back! That bell is a signal for me, not you!)

And how many words do we have to give each of those squares THREE words?

The 20 volumes of the OED contain something like 59 million words, but a vast number of them would be unrecognisable and certainly not memorable for the purposes of this task. An ordinary person has a recognizable vocabulary of around 35,000 words, although he or she would use a fraction of that in everyday life.

To get to 57 trillion combinations the number or words needed (allowing the use of the same three words in different order for different locations) is simply the cube root of 57 trillion. Or about 38,400.

So it IS feasible to cover the globe with three word strings without resorting to weird and wonderful words.

OK. Class  dismissed.