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When Numbers and Words Collide
Mike Treder   May 5, 2009   Ethical Technology  

If we had unique words for ten thousand and a hundred thousand, for ten million and a hundred million, it might make understanding of really big numbers more intuitive.

Look at these numbers:

$10
$100
$1,000
$1,000,000
$1,000,000,000
$1,000,000,000,000


Now consider these corresponding words:

ten dollars
hundred dollars
thousand dollars
million dollars
billion dollars
trillion dollars


Can you see the problem? The discrepancy? To the casual or untrained reader or listener, the ratios between between a million, a billion, and a trillion dollars do not seem intuitively different from the ratios between ten, a hundred, and a thousand dollars, when seen or heard in words.

Seeing them written out in figures does make a difference, although helping the average person understand the comparative magnitude of a trillion dollars as opposed to a billion dollars still can be difficult. But I suspect that the real problem begins with how we label (in English, anyway) the numbers that we use for counting.

Here is another list:

*one
*ten
*hundred
*thousand
  ten thousand
  hundred thousand
*million
  ten million
  hundred million
*billion
  ten billion
  hundred billion
*trillion

For the first four numbers above, we learn and read distinct words (marked *). But then as we continue the sequence, words are reused, and only every third word we encounter is new. This misleads us, unfortunately, into subconsciously assuming that the numerical distance between million, billion, and trillion is equivalent to the distance between ten, hundred, and thousand.

If we had unique words for the other steps (and those beyond them) on the list above - if ten thousand was called, say, decand, and hundred thousand was called cenand, and if ten million was called medillion, and hundred million was called mecillion, and so on - it might make understanding of really big numbers more intuitive.

Anybody want to take on this project and see it through to conclusion?  😊

Mike Treder is a former Managing Director of the IEET.



COMMENTS

Mike, why don’t you offer two brazilian dollars as an incentive?

Can we change mecillion and decillion to something else? They’re taken:
http://googology.wikia.com/wiki/Mecillion
http://www.thefreedictionary.com/decillion

A decillion equals 10^33 (but not in the British system)
A mecillion equals 10^[3(10^33) + 3)]

I suppose if we can’t come up with new terms (though I vote for Brazilian and Cotillion), we can solve Mike’s problem by just eliminating ten and hundred.

Mike, the issue with which you begin you post is our understanding of big numbers. I don’t think there are any shortcuts to this. Different countries, or rather, languages, break numbers down in different ways. The Japanese language, for example, works in powers of 10^4. But neither different words nor even writing out all of those zeroes would necessarily grant people better understanding of the numbers themselves. That comes through creative teaching, and that in turn instills creative thinking in people. For example, I like to draw a metre-long line of the whiteboard, and label the left-hand end 0 and the right-hand end 1 billion. I then ask a volunteer to quickly point to where their intuition tells them 1 million would be.

Of course, it is only 1 mm from 0 on this scale, and almost no-one (not even the professional scientists I work with) gets it right if they work so quickly that only their intuition is at work. The same demonstration works, of course for where a billion is in relation to 1 trillion.

As Richard Dawkins has observed, we evolved for “Middle Earth” - middle-sized objects moving at middle speeds in the middle distance.

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