Estimates and connected science

A very useful habit: understand the situation, pick the quantities that matter, then make a rough estimate. An estimate tells you quickly whether an answer is sensible or impossible.

How much rice does a family eat in a month? Assume all their energy comes from rice. An adult needs about 2000 to 2500 kcal a day, and you can find the kcal in 100 g of rice on the packet. Even before you calculate, you know 100 g a month is far too little and a few tonnes is far too much.

How much air do you breathe in a day? Follow the chain one step at a time:

• Breaths: about 12 to 15 a minute. A day has 60 × 24 = 1440 minutes, so about 20 thousand breaths.
• One breath: 4 to 5 breaths blow up a 2-litre balloon, so one breath is about 0.5 litre.
• Air in a day: 20,000 × 0.5 ≈ 10,000 litres.

Check it a second way. You can fill about 3 balloons a minute. 3 × 2 litres × 1440 minutes ≈ 8640 litres. That is close to 10,000, so the estimate is sensible.

Notice what science values here: careful reasoning, sometimes even more than an exact calculation. Sometimes a rough answer is all you need. Other times, such as a medicine dose, you need an exact one.

"Why do we have physics, chemistry and biology as separate subjects?" Those divisions are made by us; nature has no such walls. Take a face mask:

• Physics: how tiny particles move, and how they stick to the fibres (electrostatic attraction).
• Chemistry: the polymer fibres the mask is made of.
• Biology: the viruses it keeps out.
• Maths: how air flows through it and how much gets filtered.

Real problems need several branches together. That is why science matters even if you later choose commerce or arts: your body, your phone camera and why a cut bleeds are all science.