Why weight is so hard to guess
Ask someone how long a car is and they will be close. Ask them how heavy it is, or how many apples would balance it, and the answers spread out wildly. Weight is one of the few everyday quantities we almost never measure ourselves, and our senses give us surprisingly poor clues about it.
We see size, not mass
Eyes judge size, and size only turns into weight once you know what something is made of. A litre of water weighs a kilogram. A litre of wood weighs about half that, and a litre of steel close to eight kilograms. Two objects that look the same can differ in weight many times over.
Hands do not help as much as you might think. In the size-weight illusion, first described by the French physician Augustin Charpentier in 1891, people lift two objects of exactly the same mass and report the smaller one as heavier. The brain expects the bigger object to be heavier, prepares for it, and then reads the difference between expectation and reality as weight.
Volume grows faster than length
The most common reason for a bad guess in Tilt is the square-cube law. If one animal is twice as long as another, and shaped the same way, it is not twice as heavy. It is about twice as tall and twice as wide as well, so it holds about eight times the volume, and so about eight times the weight. Something ten times as long is about a thousand times as heavy.
That is why the gap between a peanut and a zebra feels like "a lot" but is really 300,000. We picture the zebra a few hundred peanuts long, and forget the other two dimensions.
Our sense of weight works in ratios
Psychologists have known since the 1830s, from Ernst Weber's experiments with lifted weights, that we notice differences in weight as a proportion. Adding a few grams to a letter is obvious; adding the same few grams to a suitcase goes unnoticed. That makes us good at comparing things that are close to each other and poor at very large gaps. It is also why Tilt scores your guess by how many times it is off, not by how many units.
A method that works
You do not need to know the weight of everything. You need a handful of anchors and a way to compare.
- Learn a few anchors. A paperclip is about 1 gram, a US nickel 5 grams, a litre of water 1 kilogram, an adult person around 70 to 80 kilograms, a family car about 1.5 tonnes.
- Place each object next to an anchor. Is it nearer a paperclip, a bag of sugar, a person or a car? Then nudge up or down. Think about what it is made of: mostly water (animals, fruit), mostly air (balls, empty boxes) or dense (metal, stone).
- Write both in grams and count the zeros. A 300 kg zebra is 300,000 grams. A 1 gram peanut is 1. The answer is the difference in zeros, and the leading digits do the rest.
- Check the size of your answer. If two things are a person and an armchair apart, the answer is in single figures. If one fits in your hand and the other needs a crane, the answer has at least five or six digits. Most big misses in Tilt come from skipping this step.
Two worked examples from past puzzles
A sheep in oranges (Tilt #44). A sheep is roughly a light adult person, call it 60 to 70 kg. A medium orange is about the size of a fist and mostly water, so roughly 150 g. That gives 65,000 ÷ 150, a little over 400. The real answer was 450, which scores in the 90s.
A great white shark in potatoes (Tilt #41). A large adult great white is about the weight of a small car, around 1,200 kg. A medium potato is around 200 g. 1,200,000 ÷ 200 is 6,000; the answer was 5,600, close enough for a score in the high 90s. On the day, the average score for this round was only 22.
Practice
Like most estimation, this improves quickly with feedback. That is the whole idea of Tilt: one guess, then the scale tips and shows you how far off you were. The feedback is what does the teaching, so a few minutes a day adds up. If you want to see where people struggle most, we wrote up the questions that fooled almost everyone.