Ever heard an explanation of a number that gave you an 'aha!' moment?

March 13, 2019 10:08 AM

I'm looking for examples from any subject that have made a stat/figure/number come alive. Eg: If the entire history of the earth was compressed into one year, humans would only appear in the final 24 minutes.

Can be percentages, size, age, scale, any use of numbers. Other examples that have helped me grok a figure:

•If you spend a dollar a second, it would take 11 days to spend a million dollars—but over 31 years to spend a billion dollars.
•Ants can carry 20x their body weight. If humans were as comparatively strong, a valet could pick up your car and carry it to a parking space.
•If the U.S. was shrunk to a village of 100, the richest person would own as much wealth as the bottom 90.

posted by blazingunicorn to Education (37 answers total)

As I get older I grow more and more appreciative of Tom Lehrer’s comment, “When Mozart was my age, he’d been dead for two years”
posted by Mchelly at 10:20 AM on March 13, 2019 [13 favorites]

Our amazing planet.
posted by Melismata at 10:33 AM on March 13, 2019 [3 favorites]

Cleopatra lived closer in time to the moon landing than to the building of the pyramids of Egypt.
posted by CathyG at 10:42 AM on March 13, 2019 [32 favorites]

When I was teaching A Journal of the Plague Year, I tried to make the number of deaths reported more meaningful by relating them to minutes, e.g., if one person died every second, then . . . I don't have time to figure it out right now, but my students seemed to relate to it much better than they did with just the numbers.

Also, I understood lottery odds much better when I repeatedly lost at Bingo in a room of about 50 people. Then I started thinking of it this way: If there were a drawing in my city of approximately 120,000, my chances of winning would be much, much better than my odds of winning the lottery (that's not specific numbers comparing the odds, but it still helped, and I'm sure some mathematically inclined person could figure out the real numbers for a given lottery prize).
posted by FencingGal at 10:48 AM on March 13, 2019

A million seconds is about 12 days. A billion seconds is about 32 years.
posted by Constance Mirabella at 10:57 AM on March 13, 2019 [8 favorites]

Randall Munroe, who draws/ writes xkcd, is good at this.
posted by theora55 at 10:57 AM on March 13, 2019 [8 favorites]

To accurately represent the relative sizes and distances of the Earth and the Sun, imagine the Earth as a pencil eraser. The sun would have to be the size of a basketball, and it'd be about 100 feet away, a little more than the length of a basketball court. (Saturn would be about the size of a ping-pong ball and be about 1000 feet from the Sun).

I first learned this about 35 years ago (on 3-2-1 Contact!) and it sticks with me today.
posted by skewed at 11:12 AM on March 13, 2019 [10 favorites]

Maybe this doesn't count because it's a fact about numbers, but when I was studying for the GREs a few years ago, I learned that every number can be expressed as the multiplication of prime numbers. My mind was blown.
posted by CMcG at 11:20 AM on March 13, 2019 [6 favorites]

In Maine, and other places, there are efforts to represent the solar system, at scale. I love this sort of thing and once, when I was on a roadtrip, encountered a solar system model that was not to scale, but tried, over a mile or so, and with charming hand-painted-by-kids planets.
posted by theora55 at 11:25 AM on March 13, 2019 [1 favorite]

IQ distribution is something that interests me. Assuming a normal distribution, there's likely to be someone with an IQ of over 168 in the stands at any given NFL/top college football game (rarity 1/~93,000). The Stanford-Binet scale only really goes up to 170.

Meanwhile, if you think you're a really unique genius because you qualify for MENSA (IQ > 130), you're probably not even the smartest person in the room. That IQ level is found in about 1/33 people.

You'd need to break 150 to even be 1/1000.
posted by kevinbelt at 11:44 AM on March 13, 2019 [3 favorites]

I think the thing that truly impressed on me how ridiculous multi-billionaires are was the fact that if you made 250k a year and didn't pay taxes/spend a cent of it, it would take you 4000 years to become a billionaire. FOUR THOUSAND.

This is of course putting aside investing/compound interest. But still! I make a decent salary and this was what made me realize I'll never ever ever attain that level of wealth. And why it's totally insane that we have so many billionaires and they are still getting tax breaks. WhoTF needs that much money?!
posted by sprezzy at 11:46 AM on March 13, 2019 [14 favorites]

The diameter of the fuel tanks for the Space Shuttle was determined directly, in a fashion, by the distance between the wheels of Roman horse carts.
posted by humboldt32 at 12:29 PM on March 13, 2019 [4 favorites]

Grace Hopper explains the nanosecond
posted by Glomar response at 12:34 PM on March 13, 2019 [5 favorites]

Oh, what about The Powers of 10 short film? Made big impact on me when I first saw it, which was either at the West Coast Computer Faire or maybe the Oakland Star Trek convention.
posted by humboldt32 at 1:07 PM on March 13, 2019 [4 favorites]

Maybe this doesn't count but it was a big deal for me in high school:

1/9 = .1111111111...
2/9 = .2222222222...
3/9 = .3333333333...
4/9 = .4444444444...
5/9 = .5555555555...
6/9 = .6666666666...
7/9 = .7777777777...
8/9 = .8888888888...
9/9 = .9999999999...
n/n = 1
9/9 = 1
.9999999999... = 1
posted by overeducated_alligator at 1:18 PM on March 13, 2019 [3 favorites]

I think the thing that truly impressed on me how ridiculous multi-billionaires are was the fact that if you made 250k a year and didn't pay taxes/spend a cent of it, it would take you 4000 years to become a billionaire. FOUR THOUSAND.

This is of course putting aside investing/compound interest. But still! I make a decent salary and this was what made me realize I'll never ever ever attain that level of wealth. And why it's totally insane that we have so many billionaires and they are still getting tax breaks. WhoTF needs that much money?!

This is also a helpful way to understand compound interest. If you were to instead invest it in something that returned 4% annually you would only have to wait 130 years, down from 4000. You'd of course still be dead, but let's not let that get in the way of theory.

On the other hand, if you could find something that returned 10% compound interest you could invest the 250K for one year only and go about your business, saving nothing else for the rest of your life. You would have a billion dollars after about 88 years.
posted by true at 1:19 PM on March 13, 2019 [3 favorites]

On $billionaires...

Suppose you were going to give a talk and made a big chart (e.g. of income, or taxes) such that it was 5 feet from $0 to $1 million. Extending the chart to $1 billion, would take nearly a mile (5000 ft).
posted by SemiSalt at 1:50 PM on March 13, 2019 [3 favorites]

In the 89 years since its discovery, Pluto has not yet traveled even half of its orbital period (240 Earth years)
posted by Thorzdad at 1:52 PM on March 13, 2019 [6 favorites]

Every integer greater than 6 can be expressed as the sum of 3 palindrome integers (whose digits read the same right-to-left and vice-versa.) I saw the YouTube.
posted by JimDe at 2:10 PM on March 13, 2019 [2 favorites]

Oh, I just remembered another one about exponential growth that absolutely BLEW MY MIND in fifth grade:

You are given a choice between two jobs, both lasting thirty days, both requiring intense physical labor. The first job pays $1000 a day (fifth grade me salivates), the second job starts out paying just one penny per day (fifth grade me tunes out), but doubles in salary every day.

Maybe my fifth grade class was particularly innumerate, but no one voiced any doubts about taking the first job, despite the fact that on day 30 all by itself, the salary at the second job is $5,368,709.12.
posted by skewed at 2:39 PM on March 13, 2019 [5 favorites]

A bit of an old chestnut, but the classic exponential number example (first recorded in 1256, apparently!) is obviously the rice on a chessboard story.
posted by Bloxworth Snout at 3:23 PM on March 13, 2019 [3 favorites]

This is pretty good: there are 100,000 times more stars in the universe than grains of sand on the earth; but the number of stars in the universe is about the same as the number of molecules in ten drops of water.
posted by Bloxworth Snout at 3:29 PM on March 13, 2019 [5 favorites]

The diameter of the fuel tanks for the Space Shuttle was determined directly, in a fashion, by the distance between the wheels of Roman horse carts.

Which, incidentally, means that the diameter of the fuel tanks is related to the size of a horse's butt.
posted by thecaddy at 4:02 PM on March 13, 2019 [1 favorite]

The Walton family (of Wal-Mart fame) makes as much in a minute as a typical Wal-Mart worker makes in a year. This depends a bit on how the stock market is doing and the specifics of the worker, but it has been fact checked by a reputable publication.
posted by wnissen at 4:13 PM on March 13, 2019 [1 favorite]

This whole book: How Much Is a Million? has great visualizations of a million/billion stars printed on a page, gallons of water, things stacked up on top of each other.
posted by freecellwizard at 4:42 PM on March 13, 2019 [1 favorite]

This is not quite a hard stat, but it does have to do with percentages and time, in a way....It's another example of how framing can really alter the way you look at things.

Fair warning, this made my heart break a little.

The Tail End via waitbutwhy
posted by sprezzy at 4:55 PM on March 13, 2019 [2 favorites]

Factorials (5!=5x4x3x2x1) grow incredibly quickly.

5! seconds is two minutes.

10! seconds is 6 weeks (works out evenly.)

15! seconds is 41,438 years.
posted by Wulfhere at 7:46 PM on March 13, 2019 [4 favorites]

Human eyes operate over an incredible and unintuitively large range of brightness. In the daytime, on the order of a million times more light is hitting your eye than at nighttime.

(There is even evidence that people can notice a single photon hitting their eye!)
posted by value of information at 11:41 PM on March 13, 2019 [1 favorite]

If you're seeing Celsius temperatures you can convert them to Fahrenheit with "double it and add 30." It doesn't work very far beyond this planet's temperature range but it's pretty accurate here.
posted by bendy at 3:56 AM on March 14, 2019 [6 favorites]

Sorry if this is not helpful but there is a term for this sort of thing! Social math.
posted by forkisbetter at 7:59 AM on March 14, 2019 [1 favorite]

I just saw this tweet, demonstrating the difference between the Kármán line (where space begins) and low earth orbit.
posted by bondcliff at 11:24 AM on March 14, 2019

To build on melismata’s answer, when you get down to around where sperm whales can dive, at a little less than 10k ft, you’re pretty effin deep right?! But, that’s just around two miles, which you can probably run in less than 20 minutes. We are horizontal creatures for sure.
posted by sillysally at 12:45 PM on March 14, 2019 [1 favorite]

It's often said that a deck of cards can never be shuffled the same way twice. That's because there are 52! possible combinations (52 x 52 x 50 x 49 ... x 3 x 2 x 1). But that's a rather dry way of putting it. Mayor West dreamed up a more vivid metaphor in a thread a few years ago, to answer the question of how long it would theoretically take to deal every possible combination of decks at the rate of one per second:

How long is 52! seconds?

Pack a deck of cards and a piece of paper. Every billion years, shuffle and deal yourself a 5-card poker hand. Each time you get a royal flush, buy yourself a PowerBall ticket. If that ticket wins the jackpot, place one grain of sand into the Grand Canyon. When you’ve filled up the canyon with sand, remove one ounce of rock from Mt. Everest. Now empty the canyon and start all over again. When Mt. Everest has been completely removed, make a mark on your piece of paper.

When you get to 256 marks, you've reached 52! seconds.

posted by Rhaomi at 7:24 PM on March 14, 2019 [4 favorites]

Also, in honor of Pi Day, this animation is the most intuitive explanation of why pi is 3.14... that I've ever seen.
posted by Rhaomi at 7:28 PM on March 14, 2019 [4 favorites]

The three richest people in the US – Bill Gates, Jeff Bezos and Warren Buffett – own as much wealth as the bottom half of the US population, or 160 million people.

Separately, more than half the money subject to estate taxes (inheritance tax)... has *never* been taxed before.
posted by talldean at 6:36 PM on March 15, 2019

In computer science, a bit is a single register, on or off. A byte is eight of those.

Numbers are usually stored as an integer, which is usually stored with four bytes. The biggest integer that fits in that amount of space is around four billion.

Sometimes that's not enough, so programming languages give you a 'long integer', which takes twice as much space. That's way bigger; around twenty million trillion. 'long integers' are pretty common, as they're still a tiny amount of space, but you'd never worry about the space not being big enough to store whatever you want.

And twice as much space again is bogglingly big. They're not used in most programming languages, because you'd never need anything that big.

The largest 16-byte number is 340,282,366,920,938,463,463,374,607,431,768,211,456.

Which is 3.40×10^38.

A 32-byte number could contain an integer around 10^80th.
And there are apparently around 10^80th... atoms in the universe.

TLDR: I'm semi-regularly amazed that something four times the size of "normal way to count on a modern computer" ... can be used to count every atom in every universe, one by one, without running out of numbers. Binary counting holds a *lot*.
posted by talldean at 6:50 PM on March 15, 2019

In the 89 years since its discovery, Pluto has not yet traveled even half of its orbital period (240 Earth years)

Just when I thought my heart couldn't break for Pluto anymore. What a tragic half-year it's been having!
posted by MiraK at 7:55 AM on March 19, 2019