## 18 November 2019

### A visual reminder that billions are not at all like millions

For a variety of reasons, discussions of wealth, taxes, and inequality often involve comments about the ultra-wealthy, and sometimes "millionaires and billionaires" are conflated as a group.  The image above is a reminder that a billion (of anything - not just \$) is not like a million.  It's not even a log-power larger.  In present-day usage it is a thousand millions (3 log powers) (in old British parlance a billion was a million million).

This isn't the post for arguing whether billionaires are inherently wicked or guilty of something and/or how they should be treated.  This is just a reminder about size differences.  The same perspective needs to be applied when referring to deep time (billions of years is vastly different from merely millions of years) and deep space (billions/millions of miles).

Discussed at the dataisbeautiful subreddit, where in addition to the usual analogies ("one million seconds is around 11 days, one billion seconds is over 31 years") is this even more dramatic one:  "How much larger is a billion than a million? The difference is about a billion."

1. Given that the discussion revolves around healthcare, perhaps we could use a similar comparison between a billion and a trillion?

1. You could use the same graphics, substitute the "million" for "billion", and the "billion" for "trillion", and the result would be perfectly accurate. A billion is a thousand million. A trillion is a thousand billion. Since the relationship is identical, so too would the graphic depiction of the relative proportionality.

2. Worth pointing out! Note, though, that the 'uk' billion is very much no longer a thing - a billion is a thousand millions everywhere, so far as I know.

1. Thank you - yes that's right. I've modified the text accordingly.

2. Not in large parts of Europe it ain't! The -ion/-iard distinction is the only correct usage where I'm from (the Netherlands): million = 10^6; milliard = 10^9; billion = 10^12; billiard = 10^15; etc. https://en.wikipedia.org/wiki/Names_of_large_numbers

3. While I am a conservative, I often have reminded my students that a billionaire (i.e., has just ONE billion dollars) can spend ONE HUNDRED THOUSAND DOLLARS A DAY.

For over 27 years!

If we believe in a MINIMUM WAGE, I'm not sure why that doesn't apply to the top end, as well. For all I'm concerned, let billionaires keep \$5 billion--even \$10 billion. But for goodness' sake, when we have people spending MILLIONS on a wristwatch or some piece of furniture, well, no matter how rare or artistic it is, surely putting the rest toward lifting the minimum wage or infrastructure or education, etc., is a better use of money than it doing little more than funding a billionaire lifestyle!

Besides, \$5 billion is PLENTY to start up a business that employees others.

And to think I used to be a College Republican!

4. That last one works for just about any number. How much larger is 100 dollars than 1 dollar? about a hundred dollars. How much more is a thousand dollars than a hundred dollars? About a thousand dollars.

1. Sure, it works for those. But they are not the same. In the end, 100 is 10% of a thousand, while a million is only 0.1% of a billion.

A million is truly negligible compared to a billion, whereas 100 is not negligible compared to 1000.