Saving it under a mattress is not investment, as "investment" is normally understood. It's just savings.

It's the same thing in economics. It causes the government to print more money to make up for the money missing from circulation, which will be invested. If the government doesn't do that, it increases the value of all other money in circulation.

But that’s under some weird, incorrect model of how money works. Presumably if we go down this route any further you’ll start talking about IS/LM and the money multiplier. All models are wrong, but there’s a better model that involves capital constraints and the Basel accords.

In any case, one of the major failings of modern macro is to assume you can think your way around the implications of economic actions. You have no way of knowing the consequences of stashing money under a mattress unless you actually do it, and even then there’s no guarantee the effect will be the same across different economies and in different eras. The world is just too complex for that.

Are you calling the entire field of economics a pseudoscience?

A lot of the field of macroeconomics, yes. Have you ever sat down and read that stuff?