01Science

The sky is blue because air scatters blue light everywhere

Sunlight is a mixture of all the colours. When it hits the molecules of the air, the shorter wavelengths at the blue end get knocked sideways far more than the long red ones, so blue light ends up bouncing at you from every part of the sky. It has nothing to do with reflecting the ocean, which is why the sky is just as blue over Kansas. At sunset the light crosses much more air, the blue is scattered out of your line of sight, and red is what reaches you.

One mechanism explains blue midday skies, red sunsets, and why the moon's airless sky is black.

02Ideas

The line in a fraction is a division sign, so 3/4 is 0.75

3/4 means three divided by four. Do that division and you get 0.75, which is why the fraction and the decimal are one number written two ways. Decimal places are fractions with 10, 100 and 1000 underneath, so 0.75 is 75/100, which cancels to 3/4. Percent means per hundred, so 75% is the same number again. One third runs 0.333 forever because 3 divides no power of ten.

Seeing fractions, decimals and percentages as one thing removes most of the fear people carry from school maths.

03Science

Moon phases are which half is lit, not earth's shadow

The sun lights up half the moon at all times. What changes is how much of that lit half faces us as the moon goes around the earth, a loop of about 29.5 days. Full moon means we are looking straight at the lit side; new moon means the lit side is pointed away. Earth's shadow does fall on the moon sometimes, and that is a lunar eclipse, which lasts hours rather than weeks.

You can look up on any night, work out where the sun must be, and be right.

04Science

Weather is Tuesday, climate is the average of thousands of Tuesdays

Weather is the specific report: rain, 14 degrees, wind from the west. Climate is the statistics of weather over a long stretch, commonly averaged over 30 years, including how often extremes show up. That is why one brutal cold snap tells you nothing about long term warming, and why forecasters lose accuracy after roughly a week while still saying useful things about the 2050s.

Most arguments about a hot week or a freak blizzard are really confusion between a single day and an average.

05Science

Leap years fix the quarter day the calendar leaves out

One trip around the sun takes roughly 365 days and 6 hours. A 365 day calendar therefore runs early by about a quarter day a year, and after a century your summer months would start drifting into spring. Adding February 29 every fourth year mops that up, but slightly overcorrects, so century years are skipped unless divisible by 400. That is why 2000 was a leap year and 1900 was not.

The odd 400 year rule stops being arbitrary once you see it as a correction to a correction.

05

That's the set.

All 5 of them. Pick another collection, or go back to today.