Politicians and the media are fond of dazzling us with big numbers: $62m, £35bn, $1.1 tn. All of these are unimaginable sums of money – uncountable and, for most us, unspendable. They are respectively: the launch cost for SpaceX’s Falcon 9 rocket, the anticipated ‘divorce cost’ to the UK for leaving the EU and the predicted US government annual deficit for next year based on the additional spending approved in the budget bill early this month. For most of us, winning $62m in a lottery would be a life-changing event that we might dream about but there’s only about a 1 in 14 million chance of it happening – oops, there’s another unimaginable number.
We seem quite happy handling numbers over a limited interval, from perhaps 1 in 100 [1% or 0.01] to maybe 100,000 but beyond this range our perspective ceases to be linear and probably becomes logarithmic (as in the graphic), or something similar. In other words, we don’t perceive £35bn as being about 500 times larger than $62m, or $1.1tn being about 18 million times larger. Instead, we concertina our mental picture into something more manageable, such as the image shown in the graphic. Does this have the side-effect of lessening the impact of large numbers so that we are less alarmed by costs of £35bn or deficits of $1.1tn? Maybe we would take more notice of a cost of £500 per person in the UK or a deficit of $3600 per person per year in the USA?
At the other end of the scale, something similar happens. Nanotechnology is a popular buzz word at the moment but few people can conceive of something 2.5 nanometres in diameter – that’s the diameter of a strand of DNA. It doesn’t help much to tell you that a human hair is 40,000 times thicker!
Maybe, all of this only applies to those of us who ‘see’ numbers in pictorial patterns, and to the rest of you it is nonsensical. See my post on Engineering Synaesthesia on September 21st, 2016.
Sources:
http://time.com/money/5135565/elon-musk-falcon-heavy-rocket-launch-cost/
https://www.theguardian.com/politics/2017/dec/31/tough-2017-what-does-next-year-hold-theresa-may
Financial Times, Weekend 10 February/11 February 2018.
Realize Engineering 
I often hear employees discussing football transfers and the sums associated with player moving around. I find it difficult when someone who is paid a moderate salary (say £30K) declares that buying a player for £40m is definitely worth it. I such cases I guess the value is determined by some assurance that the outcome is more certain and/or lack of a better option.