An Open Problem

Richard Feynman and Gian-Carlo Rota worked on different parts of science during their separate careers. Feynman of course was one of the most important scientists of the 20th century—see here.

His work in theoretical physics radically reshaped our understanding of the universe we live in at the most fundamental subatomic levels.

But Feynman’s brilliance was not solely due to his natural cognitive abilities. He relied on a method: a simple technique for seeing the world through the lens of open-ended questions, which he called his “favorite problems.”

Rota worked in the subject of combinatorics; and he lifted it from a barely respectable obscurity to one of the most active areas of mathematics today—to quote Richard Stanley, one of his great students. Rota had many neat results including one of the great papers Ten Lessons I Wish I Had Been Taught is wonderful. It fits neatly with Feynman notion of problems.

The Problem

Our problem today is not one that Feynman nor Rota would have most likely have worked on. Not physics and not combinatorics. But I do think it is possibly one that is still interesting. I hope you agree.

We often have to create a post so that a user can ask some particular question. The post should make it easy for them to get the answer that they are interested in without any difficulty. This is not always easy for us to make it easy.

One simple issue is this: Given a post we wish to make it easy for you to be able to ask for some particular information. The problem is that the actual post may let you get into some type of nasty state. The state may be hard to get into a place where you feel you are in control. The post may be in some strange state—one that does not respond to you questions in a way that you understand. This can be quite upsetting and led to a tough experience for your audience. This is something that we wish to avoid.

More Details

Imagine you are using our post. You interact via some application programming interface (API). You input information to the API by typing some keys or clicking on some icons. Each such input causes the API to change and enter some potentially new state. The difficulty is that this state may be a wrong one. You would like some input to force the post to reset. That is the API should change to a “reset” or some other nice state. But nothing causes this to happen. Nothing.

How can we fix the API to make that happen when we wish? This is the problem that we would like to solve.

Open Problems

This problem does have a simple solution. But the solution is not that pleasant. We could agree that some input—if you type XXX—will always reset the API. But we often do not wish to reserve a fixed sequence of inputs to always cause a reset. What if we wish to be able to input XXX in some situation? This is the problem. How do we have a way out of trouble and yet do not make the inputs restricted? The answer is not that natural we believe. What would you do?

One idea is have a special sequence like XXX that makes the reset. It does mean that XXX cannot be used in any other situation. But we could agree that XXX is replaced with a special secret sequence, that is extremely unlikely to be used except in the reset case. Perhaps we could replace XXX with the Fibonacci sequence 0112358132134 or some other special unusual sequence. Does this make some sense. It would have to be known by users and they would have to operate like this:

If the API is in some nasty case, they would say to themselves “I better type the special sequence.” Oh I recall it is 0112358132134 and the API will always reset.

And the reset will happen. Neat?