It does. When you hide money under your mattress this is equivalent of you giving your money to all the US dollar investors out there in proportion to the amount of investment they're making.

So let's just say if there is a small economy where there are only two investors you and Elon Musk, and you decide to skip investing in any business and hide money under the mattress, then this is equivalent of you giving the money to Elon Musk to invest in his business. How? Because now you're not competing him for raw materials, labor and capital.

Then when he built self-driving cars and economic growth happens because of this productive activity, when you take your money out of your mattress it is now worth more , and I'm presuming no new dollars were produced and this time.

You can see the effect if a major stockholder of a company decides to not participate in the functioning of the company, this in effect is equivalent of him lending his stocks to the other stockholders. This does not mean that somehow the company is working at a reduced power.

Hiding money in the mattress has no net effect on the number of jobs or businesses or innovation. I used to have the same reservations as you - the problem is that I was stuck on a local Keynesian/“Newtonian” view of the problem which makes it hard to predict equilibrium states. You need to switch to a “Lagrangian” view where you don’t have to manually step through all the decomposed effects of a marginal change in the money supply. A key realization is that humanity’s labor capacity at any instant is 100% independent of the number of dollars.

If you're going to be so specific about the meaning of the term investment than this is equivalent of saying that when you hide money under the mattress it is not outside the mattress.

His point was that when money is hidden under the mattress it is not serving an important function which would be if it wasn't under the mattress. I disagreed with that and explained how it worked.