2091: Million, Billion, Trillion

2018-12-28T09:43:40Z

Eckhart: /* Explanation */

{{comic
| number = 2091
| date = December 28, 2018
| title = Million, Billion, Trillion
| image = million_billion_trillion.png
| titletext = You can tell most people don’t really assign an absolute meaning to these numbers because in some places and time periods, “billion” has meant 1,000x what it's meant in others, and a lot of us never even noticed.
}}

==Explanation==
{{incomplete|This needs about a thousand years of rewriting, and I assume we'll want to do a chart of X and Y positions as with most chart comics. Do NOT delete this tag too soon.}}
Much like [[558: 1000 Times|comic 558]], this comic addresses the difficulty ordinary people have with large numbers. Though most if not all people intuitively understand the difference between one object and two objects, or one object and ten objects, or even one object and a hundred objects, as numbers increase most people's ability to innately conceive of the numbers being discussed decreases remarkably quickly. When numbers reach the millions and the billions, and especially the trillions, most people don't truly process the numbers at all, and instead conceive of them as some version of a drastically-oversimplified concept such as "very big." Where comparing one to ten is simple, comparing "very big" to a different "very big" can prove extremely challenging, and will certainly require non-intuitive, conscious thinking.

The comic represents this challenge by providing a graph which represents [[Randall]]'s ''intuitive'' conception of the values of various very large numbers, and said conception's misalignment with reality. Though some trends reflect the real value of the numbers on the graph, i.e. 100 million larger than 10 million larger than 1 million and 1 billion larger than 1 million, the curve is far from the linear (exponential on the log-scaled axes) path it should take, with 1 billion being intuitively understood as less than 100 million, based, presumably, on the fact, easily comprehended on an intuitive level, that '''100 is larger than 1''', and therefore the presence of 100 in 100 million places it at a higher value than the 1 in 1 billion would place the latter. In reality, of course, 1 billion is ten times larger than 100 million, but the comic deals not with actual reality, but with the perception of reality of these numbers '''before conscious thought is applied'''.

The most interesting parts of the graph, and the parts where the disconnect between intuition and reality becomes clearest, are the dashed sections labeled with question marks, the one between 100 million and 1 billion, the other between 100 billion and 1 trillion. Here two competing intuitive understandings compete for dominance. On the one hand, the intuitive understanding described above, with 100 trumping 1, would see the curve taking a sharp downturn. On the other hand, the path from 100 million to 1 billion is paved with such numbers as 500 million, 700 million, and 900 million, all of which would theoretically be seen intuitively as larger than 100 million, thanks to the fact that 9 is greater than 7, and 7 greater than 5, and so on, bending the curve up rather than down. These two conflicting intuitions leave Randall with no single intuitive path for the two dashed sections, leading to their dashed and questioned state.

The comic's caption and title highlight another problem surrounding the intuitive grasping of large numbers: the flaws in the English words used for them. For instance, nothing about the world "million" suggests smallness relative to the world "billion" on an intuitive scale. This unintuitive language contributes greatly to the "100 trumps 1" intuitive fallacy described above.

The title text references a classic, and highly relevant, example of a [https://en.wikipedia.org/wiki/Long_and_short_scales disconnect between British and American English]. For all English speakers, 1 million constitutes 1,000 thousands, or, said less ambiguously, 10^6. However, the definition of billion varies depending which side of the Atlantic Ocean you happen to land on. In America, 1 billion equals 1,000 millions, or 1000*10^6=10^9. [https://en.oxforddictionaries.com/explore/how-many-is-a-billion/ In Britain], 1 billion equals ''1 million'' millions, or 10^6*10^6=10^'''12''' (for those immediately asking "what did they call a thousand million, then?", the answer is the profoundly weird ''"milliard"''). In other words, 1 billion objects in England would register as 1,000 billion objects to an American, despite the fact that the number of objects has remained the same. Though people in Britain often use the American definition as of the past few decades, the fact that such a staggering difference of terminology was able to remain, and be almost completely unknown, perfectly highlights Randall's point about the failure of human intuition, and English terminology, in the discussion of extremely large numbers.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

{{comic discussion}}

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2091: Million, Billion, Trillion