Jay [jokingly]:
“The end of the world is coming!”
Molly, aged eight
[calmly spooning up another mouthful of soup]: “The end of the world has always
been coming.”
I’ll admit, I love this no-nonsense take on The End Times. I’m happy to credit my little pedant for
knowing that the sun’s core is eventually scheduled to run out of
hydrogen. Nonetheless, I’d bet that
(even if promised seventeen colors of Sculpey and The Swiss Army Knife with All
the Things), she wouldn’t be able to guess, to within an order of magnitude, when.
Is the sun is going to expand into a red giant and engulf
the Earth ‘round about 5.4 billion years from now? Or in a few thousand years? Or in a few hundred, on a Tuesday afternoon? Um…whichever.
Don’t ask Molly. This is a child
who still has trouble telling the difference between the “long ago” when many
of her classmates’ ancient ancestors crossed the Bering Land Bridge, and the
“long ago” when Ancient Mommy grew up without the Internet. Then again, don’t ask the Average American,
either. We’re not terribly good with billions.
Or even millions. Or – let’s be
honest here -- any number larger than, say, the combined total of fingers and
toes possessed by all of our Facebook friends. I’d contend that most of us are
more than a little lost in time – because most of us are more than a little
lost in math.
Okay, granted. But is this actually a problem? Really, when do most of us have to deal with
astronomically large numbers? We don’t have annual incomes, odometer readings,
bank account balances, or home values that take us past six digits. If
we’re lucky, we might enjoy, from birth to death, a grand total three billion
seconds. (A few hundred of them may be wasted on this blog, but don’t worry – a
billion is… a lot.) Is there any reason why (other than the fact that Nancy is
clearly longing to take us on a Proselytizing Adventure in Math Nerdery) we
need to haul our butts back to middle school to relearn the phrase “orders of
magnitude”?
Well, yes. For one
thing, understanding honking huge numbers comes in handy when studying minor
little topics such as, say, astrophysics, geology, computer science, chemistry,
economics, the national debt… and, oh, pretty much everything else. More
particularly, applying this comprehension of bigness to the Grand Scale of
History is pertinent with regard to two pesky topics that keep showing up in
bastions of science such as Fox News online comment threads, Kansas school board
meetings, and Congress. I’m referring, of course, to the subjects of
evolution and climate change.
On the evolution front, I promise not to draw dozens of
cladograms and start babbling about retrotransposon markers, plesiomorphies and
synapomorphies. However, I will assert that understanding how we got from
primordial soup to microwaved leftover minestrone is a heck of a lot easier if
you start with a sense of proportion. A quick primer, for those who grew
up in red states:
1.
Not only were more than seven days involved in the
process, but single-celled organisms were The Only Show in Town for about
two-and-a-half billion years of our planet’s three-and-a-half-billion-year
flirtation with life.
2.
It then took another three-quarters of the remaining
billion years before the first dinosaurs showed up (with the express purpose,
of course, of leaving their bones lying around just to trick us).
3.
Although dinosaurs were a super-recent innovation
compared to blue-green algae, they nonetheless ruled the earth for almost a
thousand times longer than human beings have existed -- and have been extinct
for a million times the run-time of The Price Is Right.
So much for evolution. As for climate change… Yeah,
I’m one of those scientists who gets paid to study this stuff. Therefore,
I can’t possibly be trusted when I suggest that Hummer exhaust and cow farts
are causing various important bits of our planet to burn, sink, desiccate, or wash
into the ocean. Meanwhile, I’ve heard head-in-the-sand climate
arguments that mix orders of magnitude like smoothies in a blender.
Yes, there was waaay more carbon dioxide in the
atmosphere 200 million years ago than there is today – and even more, 500 million
years ago. Um, yeah, climate-change
naysayers, that’s right. You win. Except that 500 million years
ago, there weren’t even any plants in North America. And, for that
matter, there wasn’t any North America. Heck, we hadn’t even gotten to
Pangaea yet. Okay, let’s simplify things. Yes, Earth has been much
hotter in the past than it is now. Yes, there has been a lot more carbon
dioxide in our atmosphere in the past. Both of these statements are
true. Both are immaterial -- because humans are not (to the nearest order
of magnitude) blue-green algae.
We are, however, within one (genetic) order of magnitude,
chimpanzees. Or (hey, close enough) rhinoceri. This, of course, amuses me immensely -- but
it also pleases me mathematically. To me, being asked to express a mathematical
answer to “within one order of magnitude” is positively delightful. It
appeals to my utterly lazy and vague nature. I don’t need to know whether
we’re talking about 43,896 red-backed-voles or 27,981 board-feet or 80, 001
heavily armed Klingon invaders; I just need to off-handedly scribble “n x104”.
However, in assigning homework and tests to undergrads,
I quickly noticed that while answers in the tens or hundreds usually came back
unscathed, things started to get ugly in the tens of thousands, and by the time
we hit the millions, it was a crapshoot. (“Now, for the grand prize of the
Jacuzzi Spa AND the Home Salon, what is the dollar value of the gross domestic
product of Cameroon, plus all extant Google stock?”) On one hand, most calculations don’t require the
level of precision that computers and calculators churn out. (If you are
measuring your height to eight decimal places, you don’t understand that “your
height” is not generally considered an atomic phenomenon.) On the other hand, once you start losing track
of where that crucial decimal point belongs, you find that you are have the
bodily proportions of a Playmobil person, or the Statue of Liberty. Those undergrads were thus subjected to
irksome tirades about why understanding orders of magnitude is a Very Big Deal.
The good news, as I told them, is that it’s really not that difficult a deal.
The bad news is… well… Fox News online comment threads,
Kansas School Board meetings, and Congress.
Our nation has a bit of a reputation – and, to be honest, it’s getting
kind of embarrassing to constantly wear the International Dunce Hat of
Mathematical Imbecility. Do we have any hope of redeeming ourselves?
Well… maybe some. Now that Molly and Lizzy have reached
the lofty academic pinnacles of third grade, their math homework is getting to
be a bit more fun than that old second-grade chaff (“Rodney wants to buy a
pencil for five cents and a ruler for twelve cents, because Rodney lives in an
alternate 1950s universe in which pennies are still actual money.”) The
other day, I asked Molly to explain her multi-digit subtraction problem, just
to make sure she really knew what she was doing. Her answer sounded so
reminiscent of the lyrics of Tom Lehrer’s classic “New Math” that I giggled
with parental pride (“Don’t worry, base eight is just like base ten, really --
if you’re missing two fingers.”)
The superb teachers at University Park Elementary are
clearly doing their utmost to make a bunch of snot-nosed, fidgety,
four-foot-high people ready to control the stock market, program your
virtual-reality holodeck, and give you a prostate exam. (Please take a moment
to think about this: that person who is telling booger jokes, dressing up in a
plastic Princess Elsa outfit, and accidentally Silly-Puttying the cat is going
to be flying your plane or performing your quadruple bypass. Okay. Now
take a deep breath and carry on.)
The twins have moved on from adding and subtracting tens
of things (“Sally has 35 toy cars and Juan has 18 toy cars. How many toy
cars will they have after they cram 11 toy cars down the bath drain and Sally’s
big sister tells on them?”) to adding and subtracting hundreds and even
thousands of things (“Fairbanks Alaska is 1521 miles from Seattle. From
Seattle to JFK New York is another 2418 miles. However, you can only fly
on free miles if you go to goddamned Newark Airport instead, and take three
trains. If the TSA spend 12.3 minutes inappropriately palpating your
teddy bear and the Long Island Railroad is suffering unexplained delays at
Hicksville, when will you get to see Grandma and Grandpa?”) In short, they are
starting to be expected to understand orders of magnitude.
In truth, I’m pretty happy about the elementary math
curriculum. Not only does it feature an ethnically diverse and
unfailingly cheerful cadre of cartoon children getting excited about the
relative heights of buildings and the capacities of conference rooms, it also
emphasizes understanding numbers, rather than simply manipulating
them. Some problems include space for kids to write out, in painfully
smudged dull pencil, answers to such stumpers as, “Is your answer similar to
your estimate?” and “Explain why your answer is reasonable”.
What? The answer has to make sense? The
pigtailed people have to be able to elucidate – in actual words – why it
makes sense? Holy subtraction, Batman.
Moreover, the kids are being offered a more holistic
perspective on time, space, and history that I recall from my own elementary
years. Not only is Molly ruminating on the age of our solar system, but
Lizzy is excited about the evolution of equines. As I tucked her in a few
nights ago, she asked me, “Do you know about Lascaux Cave?”
Yes, this piece of history takes us back only 17,300
years, not anywhere near the full 200,000 spanned by Homo sapiens -- but I’m
pretty sure that when I was her age, I was taught that history began in 1492,
and didn’t really get going until 1776.
There are ways to teach this stuff to grownups,
too. A few years back, UAF was temporary home to a wonderful display on
the history of Earth. It was, at one level, a fairly standard collection
of large, museum-quality informational boards, each one detailing some aspect
of evolution. What made the display unusual was not so much the content
of any one board, but the ratio of that content, and the placement of the
boards in relation to one another. The display was a walk through time –
set up to scale. It’s amazing how much you can learn about RNA,
prokaryotes, eukaryotes, and photosynthetic cyanobacteria when they are given
so much elbow room to accommodate their blatant lack of elbows.
As for the college students who suffered through my
courses, they were not let off the hook without a whole side-stepping foray
into the world of back-of-the-envelope calculations – a subject so delightful
to me that I’m going to save it for another lexical outpouring in which I will
babble about Enrico Fermi, piano tuners, and the Drake Equation. I’m sure you can’t wait. It will include some spectacularly humongous
numbers.
Trillions!
Quadrillions! Time and space don’t just require large numbers, they
deserve them. And we deserve the joy of wallowing in all those order of
magnitude. We -- even the little people among us -- deserve the thrill
and the challenge of at least trying to comprehend.
Jay [still
joking]: “But the end of the world imminent!”
Molly [with
patronizing patience]: “I don’t think you understand what ‘the end of the
world’ means.”
Neither do you, Molly… but you’re getting there.
Yesterday, on our walk to the school bus stop, as we
were admiring the almost-full moon hovering above the treetops, Molly asked me
if I’d caught a glimpse of the “blood moon” the night before. “No,” I
admitted, “But my friend Otto got some amazing photos. He’s way down in
Idaho, but it’s the same moon, of course.” Teasingly, I sang, “There
is just one moon and one golden sun…”
Molly looked at the moon again. “Well, just one
moon and sun that are ours,” she clarified. “Really, there are lots.”
I had to laugh.
That’s right,
kiddo. And I’m going to keep blathering away to you about the
enormity of space, and the enormity of time. Perhaps it’s idealistic of
me, but I want you to get it. Really get it in a way that’s
impossible without wrapping your head around Big Numbers. We are
pinpoints, mere asterisks in an intergalactic-sized universe– and yet, if we
turn the telescope around and look for other orders of magnitude – 10-4,
10-5, 10-6 – we are impossibly vast. Photons! Electrons!
Quarks! Hadrons! Indeed, there are so many more insanely nerdy
blog posts hidden in all that delicious numerical space…
“Yup,” I agreed. “Billions and billions.”
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