Anuva Wine Party, Powers of Ten, and Significant Figures (Digits)
Sometimes you just have to go back to the basics. Friends, food, wine.
So we invited over some people, pulled out some of our wines and had a relaxing and lovely evening. One of the greatest things about wine is its ability to be talked about and at the same time talked over.
To illustrate: the evening began with many questions about our wines and our wine club (like what is Don Juan? How did Anuva start? What does the word Anuva mean? etc.) and then progressed into a conversation over many different things, the most notable of which, in my mind, is powers of ten.
Most of you I’m sure know that powers of a number, mathematically, indicate that that number is multiplied with itself the number of times of the power. For example 10^4=10×10x10×10, or 7^3=7×7x7. The importance here is that when talking of powers of 10, once passing 2 powers of 10 or so, a human’s ability to really comprehend how big those numbers are loses touch with reality. (To exemplify this, try laying out 10 paperclips (10^1), then 100 (10^2), then 1000 (10^3). It’s very easy to write the number 10^3 but much less easy to really grasp how much that number really means).
This subject came up in relation to Alan Greenspan’s book The Age of Turbulence. In the book, Greenspan talks about how he was happy to learn that the U.S. Government used the same notation on their financial documents as the big companies that he worked for in his private consulting business. On these documents, when a figure listed as “$0.1″, this was to indicate $100,000,000. The reason for this is simply to save paper. Writing all those zeros takes up a lot of room and also.
But more importantly, this indicates, in my mind, a very big problem with how people like Greenspan, and other central bankers, view as significant figures (definition here). If people like him use 0.1 to denote 100 Million, and then 0.01 to denote 10 Million, etc., they are completely out of touch with reality. What I mean by out of touch with reality, is that since 0.1=100 Million Dollars, and 1.0= 1 Billion Dollars, and since the vast majority of the figures they are going to be dealing with would look something like “10.4″, or “16.75″, or “1.245″ at the most, this means that they do not care about anything in the 100’s of thousands of dollars (and perhaps in the Millions as well since I don’t know if they carry their figures to 3 decimal places).
As we drank our wine, we pondered what it would be like to have 100’s of thousands of dollars not be important on the financial documents of the people making the most important financial decisions in the world. I do understand, of course, that the 100’s of Billions of dollars that they deal with are much more important than the 100’s of thousands that I deal with , but I can’t help but think how much the way they simply write the numbers could affect their thinking. $100,000 could feed a lot of people, buy a lot of books or clothes, or provide other forms of care for people in need.
This is where wine took us last night.
