Power of Ten 11/21/22

Thoughts with Richard Bleil

My sleep pattern is not healthy.  I’m up way too late (or, perhaps more correctly, early in the morning), sleep in too late, and nap too often.  Yes, it’s probably all related.  Sometimes, a friend will ask me what it is that runs though my mind to keep me awake.  Well, here’s an odd thought that I had last night.

Our most comfortable number system is base ten.  We have ten numbers that we deal with most frequently (zero through nine) which is what I mean by base ten.  Mathematicians tell us that any other base that we want to use (integer based) is just as easy, if not easier.  For example, thanks to the sudden explosion of computer technology, an increasing number of people recognize a binary system, which is just base two (zero or one).  So, 101 in the binary system represents 5 in our usual base ten system.  In a trinary system (zero, one and two), 12 represents 5. 

If you think about the base ten system, it’s really rather clunky.  Ten is an even number, but half of ten is five, which is odd, and half of five, two and a half, is not even an integer.  It seems to me that a much more elegant base for a mathematical framework would be eight, as half of eight is four (an even number), and half of four is two (another even number).  You can keep dividing by two and get integers all the way down to one.  If you want a larger mathematical base, you could go to base sixteen and the same would hold true.  So why ten?

The reason, honestly, is kind of simplistic.  I’m certain it’s because we have ten fingers.  With ten fingers, base ten mathematics makes it easy to count, well, on our fingers.  Ten fingers, ten toes, base ten mathematics.  Do we still need to restrict ourselves to base ten mathematics even today as we are more intellectually advanced provided that we’re not politicians? 

Sorry, little dig there.  Meant as a joke.  Sort of.  Well, and a slight.

This makes me wonder how many other aspects of our life are based on no reason at all other than observation.  That there are 365.25 days in a year makes sense, but it wasn’t so long ago that the Earth was assumed to be the center of the universe based on the observation that we cannot feel the earth’s revolution around the sun, leading to the obvious conclusion that the sun, and all other celestial bodies, must be revolving around the earth since we can’t feel movement.  Today we are seeing a resurgence of “flat earthers”, people believing (and apparently not even ironically) that the earth is flat because they cannot see the curvature of the earth from their mother’s basement where they still live in their underwear now at the age of forty. 

Okay, I’m leaving that in there because it makes me chuckle, but I apologize to any forty-year-old flat earthers who leave their mom’s basement and still can’t see the curvature of the earth from the front lawn.  It is kind of mean, though, so I hope you’re laughing too so I don’t have to apologize for it.

It’s not always so straightforward, though.  The metric system is based on the base ten mathematical system that we all seem to love and adore, and yet, Americans refuse to transition to this system.  They insist on keeping with the English measurement system even though this system is far more difficult.  What makes it difficult is the necessity to memorize all of the common conversions (four quarts in a gallon, two pints in a quart and so forth, most of which have no rhyme or reason).  In any unit, whether it be mass or volume, there are 100 centiunits in a single unit.  Always. 

What makes the English system so seemingly simple is just repetition.  We’ve grown up with butter that has four tablespoon markings in one quarter cup stick, so we remember that.  In truth, the English measurement system is anything but simple.  Learning any new system is a challenge, but in all of the years that I taught chemistry, I can honestly say that I don’t recall any student struggling to learn the metric system

So, you might be wondering if I’m telling the truth.  These kinds of thoughts are so far left of the middle (reference to a song by the very talented Natalie Imbruglia) that it might seem unrealistic that anybody stays up late at night thinking about the mathematical system that we use.  And yet, here we are, at one in the morning, and I’m still up writing about it.


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