To get answers to some of the biggest questions in the world today, we need to have literally millions of data points and analyze them with large computers. The best example is global climate change. In order to say that the Earth is getting warmer, we must have measurements from almost everywhere, all year, for many years. You can’t just stick your head out the window and tell if global warming is happening or not.
But there are some scientific questions you can answer by just looking out the window.
One of them is the question about whether there is an infinite number of stars in the universe. Now, we have all heard about the astronomers who have looked far out into space and, starting with Edwin Hubble, reconstructed the history of the universe. But what if you don’t have a big telescope? You can answer the question anyway.
The brightness of a star decreases as the square of the distance; a star twice as far away is four times dimmer. Therefore, very faraway stars are practically invisible to most of us. But if there were truly an infinite number of stars, their light, however faint, would add up to an infinite brightness. (Hard to believe? Well, what part of infinite do you not understand?) When you look out the window and see that the sky is dark at night, you know that the universe is finite.
You could solve the problem by putting it into the form of integral calculus. Maybe I could have done so back in 1976 when I understood calculus. But you don’t need to.
There are probably lots of other fascinating scientific questions that do not require equipment, a budget, or expertise to answer.