Rounding and leftovers

Any process that converts between units, charges at several points and settles in discrete amounts will leave small quantities behind. That is arithmetic rather than anybody design.

The remainders are individually trivial and that is the problem with them. Each one is too small to be worth an action, so no action is taken, and they accumulate exactly because each individual case was correctly judged not worth bothering with.

• Moving a small amount costs a fixed amount, so the cost can exceed the thing being moved.
• A balance below whatever minimum applies cannot be acted on at all, and there is no way to top it up without a new transfer.
• It sits somewhere you had intended to stop using, which turns a closed matter into an open one.
• It is a reason to log in again, which is a reason to think about all of this again.

Decide what happens to the remainder before you start, not after. That single change removes most of the trouble, because the problem is not the amount, it is being presented with an unplanned decision at the end of a process you had considered finished.

Two decisions work. Either plan to leave it and treat it as gone, or plan to move it and accept that moving it may cost more than it is worth. Both are fine. What does not work is deciding at the time, because at the time you are tired and it is small and you will do it later, and later is when it becomes permanent.

The digit tiles on this panel are the closest thing on the board to a joke, and they are still honest. They count digits in the published onion strings, which has nothing to do with remainders.

They are here because this panel needed tiles and the board only computes two things. The alternative was to invent something about typical remainder sizes, which would have been dishonest, or to leave the strip empty, which the board does elsewhere. Showing an unrelated but genuine measurement, labelled accurately, is the third option and it is the one the design allows.

The pattern is broader than money. Any process with several steps leaves residue at each one: a small balance, an open tab, a note you meant to delete, an address stored somewhere you forgot. None of it is worth attention individually.

The general remedy is the same as the specific one. Decide at the start what happens to the leftovers, so that the decision is made when you are thinking clearly rather than when you have finished and want to stop.

It does not know what any minimum is, what any transfer costs, or how large a typical remainder is. None of that can be produced from three onion strings and a directory of text files, and none of it appears here.

What it can say is structural: remainders are inevitable, they are individually too small to act on, and the way to handle them is a decision made in advance rather than a judgement made at the end.

The specific mechanism that turns a small balance into a permanent one is worth naming, because it is arithmetic rather than policy. Moving anything has a cost that does not scale with the amount. Below some size, that fixed cost exceeds the amount itself.

Once a balance is below that line, there is no action available that improves the situation. Moving it costs more than it is worth, leaving it means it stays, and adding to it in order to move it means committing more than the leftover was worth in the first place.

That is not a trap anybody set. It is the same reason nobody posts a letter to return a coin. Knowing the line exists is what lets you avoid ending up under it, which is done by deciding in advance rather than by discovering it afterwards.