[drfuchs]

On the contrary. Take a punch-card, stick it in your 029 keypunch, and add 80 bytes of information to it by typing away. Now it weighs less than when you started. Information has negative mass.

[denton-scratch]

It has been said that a punched-card is the least-efficient form of data storage ever invented. The data is stored in the form of holes in the card. The card's only purpose therefore is to hold the holes in place, so it is 100% redundant.

[throwaheyy]

Interesting perspective. Without the card around them though, the holes don’t exist.

[lodovic]

But all the paper chips that you punched away are information too. So it's zero sum.

[bsedlm]

counter example.

consider that instead of punching out the holes, you added an ink blot, the ink is somehow reflective and thus is read by the machine (or whatever).

as the ink has a weight it now weighs more than when you started. Information has regular mass.

hence some prior assumption is mistaken and we could now prove something by contradiction.

now then, somebody please tell me if a proof by contradiction holds in constructive logic.

[drdeca]

Showing that X implies a contradiction is showing not X in intuitionistic/constructive logic, yes. However, you can’t show X by assuming not X and reaching a contradiction. By doing so you would only show not(not(X))

[rolandog]

Agreed; furthermore, your example is analogous to the classical way to answer a test by filling in the answer-sheet's circles with graphite pencils.

[amelius]

In a deterministic universe your typing doesn't add any information; any information was already there from the start.

[jrootabega]

The entire universe is holestuff and is already there by default. You add in the paper to tell the reader where the holes AREN'T.