What’s in a number? A digit by any other name would smell as sweet


With a round-number birthday coming up (next year, anyway), I thought I’d share some of my thoughts on milestone anniversaries.  I’ll take a bit of a detour through science-fiction to explain my thoughts, but I hope you’ll stick with me and that at the end of this, you’ll see these time markers a little differently.

Oh, my gosh, I’m turning 20 / 30 / 40 / 50!

For some people, birthdays aren’t a cause for celebration.  Round-number birthdays, like when you reach 40, 50, 80, or anything ending in 0, seem to cause some angst for some folks because of its perceived milestone status.

So, what if I told you that 30, 50, 90 and all of their brothers and sisters are absolutely meaningless numbers?  What if I told you that your perception of getting older based on reaching these numbers is a human construct?  These numbers are “round” and important only because of our human circumstances and evolutionary process.

Not convinced?

So, imagine that humans had evolved to have 12 fingers, instead of the 10 we have now.  You’ve probably figured out that the way we count (in English, and a great majority of human languages) is based on the fact that we have these 10 fingers.

If we had 12 fingers?  Well, our counting system would probably be a base-12 system, instead of the base-10 system we have today.  (If you’re familiar with computer programming, you’ve likely heard the terms base-8, base-10 and so forth. I’m talking about the same thing.)

“Base-10” is the technical term for counting using 10 symbols before “wrapping around” and repeating the sequence by adding one to the first column.  In other words, our 10 symbols are…

0 1 2 3 4 5 6 7 8 9
(these are the ten different symbols used to represent every number in the universe)

… and after we’ve counted up to 9, we “wrap around” and increase the first column by one and starting with 0 again:

10 11 12 13 14 15 16 17 18 19
(notice how the first column increased from zero to one)

20 21 22 23 24 25 26 27 28 29
(notice how the first column increased from one to two)

This means a base-12 system would use twelve symbols before we “wrap around”.  As an example:

0 1 2 3 4 5 6 7 8 9 χ Ɛ
(we now have twelve symbols to use before we start using two symbols to count.)

And, once we count beyond the symbols we have, we combine symbols:

10 11 12 13 14 15 16 17 18 19 1χ 1Ɛ
20 21 22 23 24 25 26 27 28 29 2χ 2Ɛ

Following me so far?

Here’s a visual aid, if you wish:

There are 13, 11 or 15 apples, depending on what you’re BASING yourself on! (Get it?)

You can view this YouTube video that also explains the base-12 system (with a bit of extra information, if you’re curious.)

A visual explanation of the base-12 counting system.

So, what does this have to do with my 40th birthday?  I’m glad you asked!

An encounter with a parallel universe

I believe so many of us put a lot of importance on our round-number birthday because of their roundness.  Our 50thh birthday might seem like a big milestone because of the jump from 49 to 50.  We also refer to decades like the 1980s, the 2010s, so a span of 10 years simply feels like a “thing”.

So, what if we were able to reach a parallel universe where humans evolved with 12 fingers, and they were counting with the base-12 system I described above?  Can you imagine some of the cultural differences that would result from that?

When you arrive in that universe, say, on your 50th birthday and you’re bummed because of your new age, one of these twelve-finger humans would do a bit of math and say:
— “What are you sad about?  You’re not old, you’re only 42 years old!”

Do you see what happened here?  The concept that we currently write as “50” is what these fictional humans would write as “42”, a ways away from that round-number birthday.

Or, you could perhaps imagine running into an alternate universe woman who’s happy that she can retire with full pension because she’s 60 years old today.

You do a bit of math and realise that what she calls “60” is “72” using our numbers symbols. 

— “Wow,” you say to yourself, “people get their pensions in this universe at age 72! What a long time to wait.”

The day the Earth spun faster: another example

Perhaps the twelve-fingered humans didn’t convince you.

What if we imagined, instead, that Earth spun around the sun faster than it does today?  All other variables would stay the same (the same number of fingers, the same base-10 counting, the same day length, and so forth), but the year on this imaginary planet was only 10 months of 30 and 31 days.

So, let’s cross into a portal and meet our fast-planet brothers and sisters.  We walk down the street, and everything seems to be the same.  We greet a fellow strolling by and ask his age.

— “I feel kind of old.  I turned 40 today.”

When you remember that this planet’s year is shorter than yours, you realise that your new friend isn’t as old as you might otherwise think.

Remember, for this fellow, a year “ticks by” two months sooner than it does for you.  The same amount of objective time passes for both of you (24 hours is the same for both of you, for example), but because this pretend planet revolves around the sun faster, these humans’ birthdays come more often than they do for us.  If we use the 12-month calendar you and I are familiar with, the man you just met is 80 months younger than his “40” would seem.  So, who’s right: him for feeling old at “40”, or you for thinking he’s a young’un’ of 33 “normal” years?

What all this means

I’m convinced that our perception of time and of ageing are largely influenced by many factors that shaped our society.  Like in the example above, if we had 12 fingers, what we perceive as a “round number” would be different, and different birthdays would have that “big deal” feeling.

What if our planet didn’t have a moon? The concept of a “month” would be different or non-existent.

What if our planet revolved around two suns? Would we celebrate birthdays after going around one of the suns, or both?

What if we didn’t have fingers or hands, but claws instead?  Would we count using a base-4 system? (Our number system would “wrap around” much quicker, and we’d reach 3-digit numbers pretty quickly.  Our base-10 “16” would be written “100” in base-4, so would our teenagers feel ancient in such a universe?)

So, here’s what I’m getting at:
These numbers that make us feel so old, forget about them!  They’re completely random! They’ve grown out of thousands of years of evolution and have meaning engrained in them because we’re surrounded by them all the time.  One small difference in the history of humans could have completely changed our perception of these numbers.

Think about that when your next birthday comes up.

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One thought on “What’s in a number? A digit by any other name would smell as sweet

  • Lorna

    That is an interesting concept! I thoroughly enjoyed reading and understanding the difference between the base 10 and base 12 counting. I have never felt the wish to be younger than I am nor have I dreaded birthdays whether they were marking a decade or not. I guess being a number person I liked looking at them in a different way. Hope all is well with you both.