Random Rambling: Math (Scale)

We have... let's say an eclectic mix of interests, and we feel our patrons do too.  With that thought in mind, we present a feature we call "Random Rambling."  It isn't quite random, but it's close:  we made a little spinner with some of our favorite subjects.  Every Friday, we give the thing a spin, and then you, lucky people that you are, get to learn a fact related to the subject the spinner landed on.

This week's topic is:

Math!  ...Barely.

So let's talk about scales.

People suck when it comes to scale.  It's a result of biology; we're designed to be really good at estimating distances by eye, but as a result, anything too small to see and anything too big to see just goes over our heads.  For example:  without looking it up, guess how many cells there are in your body.  For reference, the average human cell is just a little bit too small to visually perceive.  So just imagine the smallest possible thing you could see, then imagine something a little smaller than that, and then estimate how many of those it would take to make your body.  Don't even worry about being super accurate, we'll give you full credit if you are within an order of magnitude of the correct answer.

Got it?

40 trillion.

For the record, we asked the people closest to us the same question.  We wanted to be fair about how likely it was that someone reading this guessed correctly.  Answers ranged from "2 million" to "7 billion."  If you guessed somewhere in that range, you aren't alone.  But we aren't done.  Are you ready for round two?

Guess how many atoms there are in a typical red blood cell.  We say "red blood cell" in particular because the difference between the smallest and largest cells in your body are a factor of 30 to 40; that's enough that, if we asked for an "average cell," depending on which you picked you could get a "wrong" answer even if you were 100% accurate.  So:  typical red blood cell.  We'll help you out:  a red blood cell is 8 micrometers long (there are a thousand micrometers in a millimeter) and has a volume of about 100 femtoliters (there are a quadrillion femtoliters in a liter).  Based on that mental image, how many atoms do you think are in a red blood cell?

Drum roll...

Answers ranged from "ten thousand" to (suspecting that the lesson here was "always guess bigger") 5 quintillion.  Actually, using the same number as last time would have been your best bet, because the actual number is about 100 trillion.  That's well within an order of magnitude of 40 trillion, and close enough that you could reasonably say, "There are about as many cells in a body as there are atoms in a cell."

The funny thing about that is we're willing to bet you remember that quote way longer than you remember the correct number for each answer.  Because we're so bad at scale, you see.  40 trillion and 100 trillion just feel wrong.  Those aren't real numbers, says your hindbrain.

Here's one that is often used to try and show people just how rich the richest people on the planet are.  Say that you get yourself a job that pays really well.  As in, "You will now earn $1 per second, forever," good.  That's $60 a minute!  $3,600 every hour of the day!  More than $600,000 each and every week!  And, looking it up via Google, Elon Musk is worth $684 billion dollars.  If his wealth didn't change and you never spent any of your money, how long would it take you to have as much money as he does?

Dramatic pause.

Answers ranged from "12 years" to "I don't know, stop asking me questions!"  After being tied down and having red-hot pokers applied, they guessed 31 years.  The correct answer is a little shy of 22,000 years.  For reference (because, as we've established, people are bad at scale) that's several times longer than all of written history.

Eat the rich, folks.

One last question for you.  This time we'll flat out tell you the numbers involved, and all you have to do is estimate the last one.

Earth is, depending on the day, between 90 and 95 million miles from the sun.  Earth is also about 8000 miles wide, and the sun is a bit north of 800,000 miles wide.  The nearest star system to ours, Alpha Centauri, is 4.25 light-years away.  For reference, a light-year is the distance light in a vacuum can travel in one year.  Rather than do the math, we'll just tell you that the distance to Alpha Centauri the equivalent of about 25 trillion miles.

You decide to build a scale model of this arrangement, and for the scale, you've decided to set the "Earth to the sun" distance to one single foot.  At that scale, which is 500 billion:1, Earth would be 1/1000 of an inch wide.  For reference, a red blood cell is about the same size.  (Isn't it neat how these scales sometimes line up?)  The sun, 100 times wider, is a little smaller than a pea.  Be careful not to look directly at the pea; it's more than bright enough to blind you.  At this scale, where should you put Alpha Centauri?

One final gap to keep you honest, and...

Answers ranged from 10 feet to, this person feeling a little ridiculous, guessing 5,000 feet.  The correct answer?  Our scale model would have a 1-foot gap between the Earth and the Sun, and the Alpha Centauri system would be some 50 miles away.

Like we said.  People suck when it comes to scale.