The game
What is the Size It Up game?
Size It Up is a “guess the size” game: a silhouette stands beside a familiar reference object, and you resize it until the scale looks right.
It is visual estimation with nothing to read and nothing to remember. No numbers are typed. You judge real-world scale the way you would across a room, by comparing one thing with another, and then the outline snaps to its measured size and shows how far your eye was out. That is the whole game: guess the size, commit, and watch the outline correct you.
Each run deals 5 of these comparisons, and you can start another whenever you like. A size guessing game sounds like a test of knowledge, but it is closer to a test of perception, and perception makes the same mistakes in everybody. The rest of this page is about those mistakes and how to correct for them.
To practise estimating with numbers instead of by eye, try the Fermi game: break a question into quantities you can picture, make an educated guess and check the worked answer.
- comparisons in a run
- 5
- off or less scores a perfect round
- 5%
- too big or too small scores nothing
- 4×
The name
Where does "size it up" come from?
The word size began in a courtroom, not on a ruler.
Size reached English around 1300 from the Old French sise, a clipped form of assise, the assize: a sitting of judges, from the Latin assidere, to sit beside. An assize fixed things by ruling, among them weights and the portions of food, and the sense moved from the ruling to the amount it fixed, and so to how big anything is. Both senses were already in use in English by about 1300.
To size up, meaning to estimate, to assess, to take the measure of, is American slang of the 1800s: the Online Etymology Dictionary dates it to 1847, Merriam-Webster and the Oxford English Dictionary to 1884. It has always meant a judgment made by looking, before any tape measure comes out. The game takes the idiom literally: you size an outline up against a yardstick, commit, and find out how good the judgment was.
Why it is hard
Why is it so hard to guess the size of something?
A century and a half of psychophysics, the science of how sensation tracks the physical world, says the errors are built in.
Eyes measure ratios, not gaps
Ernst Weber showed in the 1830s that the smallest difference you can notice grows in proportion to the thing itself: a centimetre matters on a coin and vanishes on a bus. Gustav Fechner built that into a law in 1860. It is why this game scores a guess as a ratio.
Area is under-read
In 1957 the Harvard psychologist S. S. Stevens set out the power law of sensation that carries his name. In the table of exponents he later compiled, apparent length grows in step with real length, an exponent of about 1.0, but apparent area lags with an exponent of about 0.7. Double a lake's area and it does not look doubled, so large places get guessed too small.
The extremes get flattened
H. L. Hollingworth described the central tendency of judgment in 1910: within any set of sizes, people overestimate the small ones and underestimate the large ones, pulling every guess towards the middle. If a whale already feels enormous, it is probably bigger still.
Illusions
When the eye gets size wrong on purpose
Some of the oldest tricks in perception are about size, and each one explains a mistake you can make in a round.
The Moon illusion
The full Moon looks far bigger just over the horizon than high in the sky. A photograph shows it no bigger; if anything it is about 1.5 percent smaller, being further away by roughly the radius of the Earth. Aristotle mentioned it, Ptolemy wrote about it, and there is still no single agreed explanation. What the Moon sits next to changes how big it looks.
Ebbinghaus circles
Two identical circles, one ringed by large circles and one by small ones: the first looks smaller. The figure carries the name of the German psychologist Hermann Ebbinghaus and was made famous by Edward Titchener's textbook of 1901. It is the reason every round gives you one reference object to judge by.
The Ponzo illusion
Lay two equal bars across a pair of converging lines, like railway tracks running away from you, and the bar nearer the point where they meet looks longer. Mario Ponzo described it in 1911: the brain reads the lines as depth and enlarges whatever seems further off.
The Ames room
A room built crooked so that, through one peephole, it looks square. A person walking from one corner to the other seems to grow or shrink as they go. Hermann von Helmholtz described the idea in the 19th century, and the American Adelbert Ames Jr. built the version that carries his name. Film-makers still use the same forced perspective to make actors look different sizes.
Stonehenge, 18 inches tall
Not an illusion, but a size mistake quoted ever since. In This Is Spinal Tap (1984) the band's Stonehenge stage prop arrives 18 inches tall, because the sketch said 18 inches where it meant 18 feet. A number means nothing until you know what it is measured against.
Maps
Why countries look the wrong size on a map
Most people learn the shapes of countries from a map drawn to steer ships, not to compare land.
Gerardus Mercator published his projection in 1569 so that a constant compass bearing would plot as a straight line. The price is area: the map stretches everything as it nears the poles. Greenland looks about as large as Africa on it. Africa is about 30.4 million square kilometres and Greenland about 2.2 million, so Africa is roughly fourteen times bigger.
That is why the places in Size It Up are compared by their measured area and not by how a wall map draws them, and why a northern country, state or lake is so often smaller than your guess and an equatorial one larger.
- Africa
- 30.4M km²
- Greenland, which the Mercator map draws at a similar size
- 2.2M km²
- how much bigger Africa really is
- about 14×
The method
How to guess the size of anything by eye
Four moves, the same ones a surveyor or a painter makes without thinking.
01
Start from the reference object
Ignore the drawing's size on screen. The yardstick beside it is the only thing in the frame with a known measurement, so every judgment starts there.
02
Count in yardsticks
Ask how many of the reference would fit along the thing: three people tall, two buses long. A count of whole units is easier to trust than a figure in metres.
03
Check the other direction
A silhouette has a height and a width. If your length implies something absurdly thin or squat, the length is wrong.
04
Then push past your instinct
Correct for the known biases: nudge big things bigger, small things smaller, and anything measured by area further than feels comfortable.
| Within 5% of the real size | 100 points |
|---|---|
| A quarter too big | 81 points |
| Half again too big | 63 points |
| Twice the real size | 37 points |
| Half the real size | 37 points |
| 4 times out, either way | 0 points |
Twice too big and half too small earn the same score because they are the same mistake: one doubling away from the truth. Scoring the ratio, not the gap, also means a beetle and a battleship are marked alike.
A short history
How people have shown scale, from the cubit to Powers of Ten
Every age has needed a way to say how big something is, and most of them began with a body or a picture.
Antiquity
The body as a ruler
The first units were reference objects everyone carried: the cubit from elbow to fingertip, the foot, the fathom of two outstretched arms. The hand, four inches, still measures horses.
1569
Mercator's map
A projection made for navigation fixes the mental picture of country sizes for centuries.
1638
The square-cube law
Galileo shows why a giant cannot simply be a scaled-up man: area and volume outrun length.
1800s
"Size up"
The phrase enters American speech in the sense of estimating by eye: 1847 by one dictionary's count, 1884 by two others.
1860
Fechner's psychophysics
Weber's finding becomes a law: sensation follows the ratio of a change, not its amount.
1910
The central tendency of judgment
Hollingworth shows guesses drift towards the middle of whatever range is on offer.
1957
Stevens, and Cosmic View
Stevens sets out his power law of sensation. The same year the Dutch teacher Kees Boeke publishes Cosmic View, a book that steps through the universe in jumps of ten.
1977
Powers of Ten
Charles and Ray Eames turn the idea into a nine-minute film, after Canada's Cosmic Zoom of 1968. It entered the United States National Film Registry in 1998.
Beyond the game
Who sizes things up for a living
Judging scale against a known object is a working skill in more trades than it seems.
Artists
A pencil held at arm's length is a portable reference object: painters use it to compare the height of a head with the width of a shoulder before a line is drawn.
Field scientists and photographers
Archaeologists, geologists and forensic photographers lay a scale bar in the frame, because a photograph of an object alone says nothing about how big it is.
Astronomers
The Sun and the Moon look the same size from Earth although the Sun is about 400 times wider. It is also about 400 times further away. Apparent size is always real size divided by distance.
The skill can be trained. A 2006 study in the Journal of Research in Science Teaching, by Tretter, Jones and colleagues, asked 215 people from fifth grade to doctoral students to judge the sizes of things across the full range of science. They found people grasp relative size more readily than exact size, and that the accurate ones lean on a stock of landmark objects. A yardstick beside every silhouette is that finding turned into a game.
In this game
How Size It Up turns a judgment into a score
Every rule in the game follows from the science above.
Guesses are marked as ratios because that is how eyes work. A guess within 5% is perfect because that is about the limit of what a drag on a phone screen can express, and one 4 times out scores nothing. Places are compared by their measured area, never by how large a wall map draws them. And there is always a yardstick, because relative size is the judgment people can actually make.
Vocabulary
Scale terms, defined
The words for judging, drawing and comparing how big things are.
- Silhouette
- The filled outline of a thing: its shape with the detail removed, so only proportion is left to judge.
- Reference object
- Something of known size set beside the unknown. In this game, the yardstick on the left of every pair.
- To scale
- Drawn so that every part keeps its real proportion to every other. Both outlines in a round share one scale.
- Ratio error
- How many times too big or too small a guess is. Twice and half are the same ratio error.
- Equal-area
- A way of drawing a place that keeps its area honest, unlike a navigation map that inflates the far north and south.
- Forced perspective
- Placing things at different distances so that they seem to be a different size, the trick behind the Ames room and many a film set.
- Size comparison game
- A game that sets two things side by side and asks how big one is next to the other. In Size It Up you answer by resizing a silhouette beside a yardstick, with no numbers to type.
- Apparent size
- How big something looks from where you stand: its real size divided by its distance.