Or how a lot of time is wasted. For example on perpetual motion machines and infinite data compression.

A lot of major scientific discoveries were made while people were trying to turn base metals into gold; also known as alchemy.

Some examples include discovering phosphorus, the identification of arsenic, antimony, and bismuth as elements rather than compounds, and the development of nitric acid, sulfuric acid, and hydrochloric acid. Alchemy ultimately evolved into modern chemistry.

I think the key is that thinking that something is a waste of time is the type of mentality that prevents individuals from pursuing their interests to the point where they actually make important discoveries or make great inventions.

If you put enough time and energy into anything you're bound to learn a lot and gain valuable insights at the very least.