I've told you a million times!

October 31, 2009 5:57 AM

What are your benchmarks for estimating/comprehending quantities? I'm terrible with magnitudes; if someone tells me that they weigh 85kg, or that they come from a city of 2 million people, this doesn't create a mental picture for me at all; they might as well be speaking another language. After a lifetime of being resigned to this, I've decided I'm going to familiarise myself with a list of benchmark quantities: my height, the height of my tallest friend, population of my city, etc. Help me compile a list of quantities I should be familiar with, and tips for learning to come to grips with quantities!

For example, these are some of the quantities I'm going to familiarise myself with:

Population of Australia: 21 million
Population of USA: 304 million
Population of China: 1.33 billion (1,330 million)

My height
Height of tallest friend
Height of short friend

My weight
Weight of buffest dude at my gym

Population of my city
Population of all cities I've lived in

GDP of Australia
GDP of major nations

Distance from my house to the corner shop
Distance from my house to work
Distance to other cities

Any quantities that you find useful, or tips for better visualisation, would be appreciated. Thanks!

posted by surenoproblem to education (26 comments total)

A gallon of milk weighs eight pounds.

The Chicago Metro theater has a standing capacity of 1,000 people.
The University of Michigan stadium seats a bit over 100,000 people.

A mile is 20 New York City blocks and takes about 20 minutes to walk at a brisk pace.

A '100' cigarette is so-called because it is 100 millimeters long.
posted by meadowlark lime at 6:09 AM on October 31, 2009 [1 favorite]

A CD is 12 cm across.
posted by Zarkonnen at 6:20 AM on October 31, 2009 [1 favorite]

Rob at Cockeyed.com put together a photographic height/weight chart that might help you with learning how weight correlates with size.

For city sizes, something I did over time was learn the sizes of smaller towns and cities that I was familiar with. When I hear of a new place that has, say, 50,000 people, I have a few reference points in my head for what that looks like and feels like. I guess you have the "all the cities I've lived in" on the list, but not knowing how many that is, you could also add neighboring towns, etc. I find it really helpful when reading a story or something and I see a statement like "A sleepy town of 10,000 souls" and I immediately have a mental image of what kind of a place it is.
posted by cabingirl at 6:34 AM on October 31, 2009

The infochimps list of Scale Landmarks is helpful.

Also, Wolfram Alpha will convert many measurements into more intuitive measurements (eg 35 cm)
posted by James Scott-Brown at 6:47 AM on October 31, 2009

Size of pea, golf ball, tennis ball, grapefruit. Useful for describing tumors.

A quick comparison is that

100 kg = 220 lbs
thus 50 kg = 110 lbs and 75 kg = 155 lbs

When they ask my weight at the doctor's office, I like to say "100,000 grams".

Normal human temperature is 38 degrees Celsius. Thus any description of temperature over 30 C can be regarded as pretty warm.
posted by yclipse at 7:20 AM on October 31, 2009

I alway found it useful to remember that

1 liter of water = weigh 1 kg( 2.2 lbs)

so 100 kg person weighed same as a bag of 100 liter water!
posted by Carius at 7:47 AM on October 31, 2009

Average weight of a newborn baby is a useful one for joining in conversations when someone has just sprogged, a la "Ooh, what a whopper!" (substitute more tactful version if new parent actually present). Don't know what that weight actually is - in my head its about 6 or 7lbs.
posted by penguin pie at 7:53 AM on October 31, 2009

As a suggestion, I don't think you want to think about the population of the US (for example) as 304 million. When you are trying to get a sense of scale, it's better to err on the side of being inaccurate and of remembering more things. So 300 million works well, and 4 times that for the population of China. For Australia, 20 million is good. In other words remember easy-to-manipulate numbers to within ~20% and leave it at that.

I think you develop a set of quantities that are useful to you personally if you do a lot of practice calculations using those quantities you know. If you are interested in public policy, then you will develop one set, and if you are interested in biology you will develop another. But you will remember them best if you keep them simple and use them a lot. For practice, Google "Fermi questions." When you are actually doing the calculations, stay sloppy so that you can do them in your head: 7x6=40; 9x9=100; 80/9=10.

A point that is often made about doing calculations like this that the errors tend to self-correct in the sense that chances are that as many of the numbers you use will be high as low.

One way I remind myself about the difference between a million and a billion is that when I was ~10 days old I had my millionth heartbeat; I was ~30 years old when I had my billionth. (Note that different countries use different definitions of a billion; this is for the short scale billion.)

Distance to the moon: 250,000 miles.
Width of US: 3,000 miles.
Diameter of the earth: 8,000 miles.
Circumference of the earth: 24,000 miles
Pi: 3
e: 3
Distance to the sun: 100,000,000 miles
Width of a time zone at the equator: 1,000 miles
At 30° latitude: 1,000 miles
At 45° latitude: 700 miles

1 fist held at arm's length = 10 degrees
1 finger = 2 degrees
(So if the sun is three fists above the horizon in the afternoon, for example, it is 30° away from sunset. This is one part in 12 of 360°, so sunset is in two hours. Put another way, a fist is 40 minutes and a finger is 10 minutes.)
posted by Killick at 7:59 AM on October 31, 2009

This is more in the tip/learning category, but there is an interesting book called 'Consider a Spherical Cow' that discusses methods of estimation. It's targeted more at students of science, but it has some nice approaches for detailed questions. I mentioned it in this thread previously, which is quite similar to your question.
posted by a womble is an active kind of sloth at 8:06 AM on October 31, 2009

More weights and measures previously and via xkcd.
posted by Dave 9 at 8:07 AM on October 31, 2009

A US nickel weighs five grams. I don't know how useful that will be if you're not in the US, though.
posted by trip and a half at 9:23 AM on October 31, 2009

A compact car weighs around 1 ton = 2000 pounds.

The distance around a standard running track is 1/4 mile.
posted by Salvor Hardin at 9:30 AM on October 31, 2009

Wikipedia has a good set of pages on orders of magnitude:
length, time, mass and others. And if I might pimp my own FPP on this subject, there are some good links in the comments there as well.
posted by Electric Dragon at 9:44 AM on October 31, 2009

I find humans visualize many things better through metaphor than through facts and numbers. If you state the Earth has this diameter, the moon that diameter, and this is how far apart they are, most people are no closer to enlightenment than before. If you ask two people to stand ten feet (or three metres) apart, one holding up an orange and one holding up a grape, you have achieved a much more concrete representation of the relative sizes and distances.
posted by ricochet biscuit at 9:49 AM on October 31, 2009

A cube of water 3 feet on a side weighs about 1 ton. (Useful for estimating how heavy that "small" aquarium is...)

In the US, a 5lb sack of flour makes for a good weight reference. Similarly, a full 2-liter bottle weighs roughly 5lb, and a now-standard 20oz coke bottle is a pound and a quarter.

If you're over 30, the floor tiles you saw all through grade school were probably 9x9" (and contained asbestos). Most renovated building have 12x12" tiles, which makes estimating the size of a room quite easy -- the graph paper is already installed on the floor. Knowing the length of your own foot and your stride length makes quick estimation easier, too.
posted by range at 9:51 AM on October 31, 2009

Oh right, and I forgot my favorite conversion factor -- light travels about 1 foot per nanosecond.
posted by range at 9:53 AM on October 31, 2009

I'd say that rather than trying to memorize a bunch of trivia facts, you just pay more attention to observing the things you see from day to day. Example: the gallon jug of milk in the fridge. How heavy? about 8 lbs. How big in physical size?

So now when you see a container full of water, you can mentally estimate how many jugs of milk would fit in there and how heavy that's going to be to pick up.

Also when someone mentions units to you, try to relate that to something you know already. How much water spilled on that electrical cabinet? About a pint? Hm. Doesn't mean anything to me until I picture "a pint" = "a beer glass"

When you're at a sporting event or concert, observe how big the crowd seems. Then find out what the attendance was. Really it's not about memorizing numbers, it's just being observant enough and for long enough that you start to get a "gut feel" for wild-ass guesses.
posted by ctmf at 9:58 AM on October 31, 2009

Your arm span is about your height. Measure out ten feet with visual markers, stand in the middle and stretch out your arms. See how much gap on both sides. It's pretty sloppy measurement, but it helps me estimate stuff like "no parking within 50 feet of fence" or "I have a 50 ft. cord, can I reach that with the weed whacker."

Actually the last one turned into stretching out the 50 ft. cord and just standing back and looking at how long it was. Now 50 feet is a unit of length I can use for estimating things visually by imagining if my cord would reach it once, twice, etc.
posted by ctmf at 10:03 AM on October 31, 2009

A professor I had told us that his son had a job doing a census of alligators in Florida. They spent a lot of times looking at sticks from various distances and then measuring them so that they could estimate lengths of alligators in the swamp from a safe distance.

Also, when my kids were learning to estimate and understand mass, length, etc., the teachers had them go around the house and measure table legs, toys, books, each other, as well as weigh all kinds of things. They made little lists and it helped give them a frame of reference.
posted by artychoke at 10:59 AM on October 31, 2009

A standard paperclip is supposed to weigh about a gram, I've heard, but a gram is so light that I don't find that very useful, so that nickle suggestion sounds good to me.
A pint's a pound the world around.
posted by Mngo at 11:13 AM on October 31, 2009

I'm mostly familiar with areas and lengths, so here are some I have in mind for scale:

A u.s. dollar bill is exactly 6" long.

The playable area of a pro football field is 360 feet by 160 feet. That is almost exactly 1 1/3 acres. So 4 acres is the area of three football fields.

A generous parking space is 10 feet by 20 feet. Narrow spaces might be as thin as 8.5 feet.

A row of double sided parking is 60 feet wide, about the same width as a basketball court including the out of bound space on each side.

A story on a building is generally about 10' tall in residential uses and 12' tall in other uses.

Gas is about 6 pounds a gallon, diesel is about 7 pounds a gallon, water is bit over 8.
posted by meinvt at 12:01 PM on October 31, 2009

Use your own body for lengths. One of the most useful things I took out of high school science came from an exercise where we found dimensions on our hands/arms that were a centimeter, a decimeter, and a meter. So now I know that, on me,

My index fingernail is about a centimeter across
My index finger is about 10 centimeters long when held a particular way
My nose is close to a meter from the tip of my outstretched hand

This comes in useful all the time.
posted by lostburner at 12:44 PM on October 31, 2009

1 foot x2248 1 nanosecond (@C)
posted by spasm at 1:28 PM on October 31, 2009

Hey, the html worked in Live Preview. I meant approximately equal (x2248).
posted by spasm at 1:29 PM on October 31, 2009

For populations, I find it far easier to think about density rather than pure numbers. China, the US and Australia have roughly the same area, right? So, the US (at ~300m) has about 15 times as many people as Australia (at 20m). Well, in Australia I can drive for hours along the coast and come across a few towns. I can drive for a few days through the outback and come across a cattle station or two. Multiply that by 15- the towns you drive by will be more common, and have more people. The empty deserts will be there, but they'll be 15 times smaller.

Same thing for China- you know how the US will have reasonably large towns all over the place, and a few large areas with not many people? Well, China has about 4 times as many people as the US. So, shrink down the open areas of the US, double the size of the towns and villages, and cut down the distance you need to travel between them.
posted by twirlypen at 4:32 PM on October 31, 2009

number of horns on a unicorn acre = 7.76750034 × 1024 US teaspoons per light year
posted by MaxK at 8:54 PM on October 31, 2009