Two Kinds of Numbers

Big and little? Odd and even? Real and imaginary? Integer and fraction? Prime and composite?  Irrational (like pi and the square root of 2) and whatever the other ones are?  Sorry, my half-remembered-because-almost-never-used numerical education extends no further than that: I can generate no more dichotomies, true/false or otherwise.

But the sad limits of my numeracy are no matter here. According to Scientific American, the two kinds of numbers are these: interesting and boring. Well, technically, it’s the positive integers that are either interesting or boring, not *all* numbers, but for day-to-day purposes for most of us, it amounts to the same thing.

You will be relieved to know that we’re not going to go into this in detail–there being the same two kinds of blog posts as positive integers–but there is just one thing I thought you might find, well, interesting. In 1963, a mathematician was looking for integer sequences for a calculation he was doing and could find no comprehensive list thereof. Go, um, figure.

And so, ten years later, Sloane published his first encyclopedia, A Handbook of Integer Sequences, which contained about 2,400 sequences that also proved useful in making certain calculations.

Now, this book does not have a place on my bookshelf, and possibly not on yours either, but we could be the outliers.

The book met with enormous approval: “There’s the Old Testament, the New Testament and the Handbook of Integer Sequences,” wrote one enthusiastic reader, according to Sloane.

Lately, unconstrained by physical publication costs (or shelf space), the Online Encyclopedia of Integer Sequences (OEIS) has taken up the cataloguing challenge.

As of March 2023, it contains just more than 360,000 entries.

It is this searchable OEIS that provides the data for determining whether a given positive integer is interesting or no: the more often a number appears in an integer sequence, the more interesting it is deemed to be. And here’s the interesting bit about *that*: the citations are not evenly or randomly distributed. They have a pattern. Based on citation count, the numbers fall into two bands. Moreover, for numbers larger than 300, the gap between the bands is clear, with roughly 20% being interesting (aka cited often) and 80% being boooring (aka cited rarely).

But why are they differentially cited? You will not be astounded to learn that it’s because people find some numbers more interesting than others, and that people like to study the interesting ones.

So the split into interesting and boring numbers seems to stem from the judgments we make, such as attaching importance to prime numbers.

Yes! This, I can get behind.  The interesting-ness of numbers is not an inherent quality, it is something we put into them. After all this time, it’s good to know that numbers are the same as everything else in life: We get out of them what we put into them.

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8 Responses to Two Kinds of Numbers

  1. Jim Taylor says:

    You must have been EXTREMELY BOOOOOOORRRRREEEDDD even to venture into this territory!

    Jim T

  2. Mary Gibson says:

    Yes. Over my head as well and vaguely unsettling. But what we find interesting….I have no interest in what lies under the hood of my car. But understanding information technology…THAT’S inherently (defined as the quality I put into it) interesting.

    • Isabel Gibson says:

      Mary – I guess if we weren’t different, we’d have very advanced cars and no computers. Or the reverse . . . Sometimes I wonder why we’re so different, but I’m not sure why I think we should be the same.

  3. I am surprised that Sloane’s Handbook of Integer Sequences was not on my father’s bookshelf. Or perhaps it was and now lies hidden in the dozen or more boxes of books my sister left that I have not investigated. We may be the outliers, interested in words before and beyond numbers. Our numbers (oops!) are dwindling, according to a recent report on the percentage of university students opting for degrees in English and the Humanities. We may take solace in the knowledge that our main method of communicating is more widely descriptive, more useful socially, and more (as you say) humane.

    • Isabel Gibson says:

      Laurna – I am comforted by the knowledge that all children raised in anything like a normal environment have language as a birth right. Arithmetic, not so much.

  4. barbara carlson says:

    AI could have done those 2,400 sequences in 32 seconds… with pictures.

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