The Halting Problem (Part One)
A plan is a list of things to do.
When a computer runs, it is doing the things that are written in a plan.
When you solve a problem like 23 × 3, you are also following a plan.
Plans are made of steps.
To follow a plan, you do what each plan step says to do, in the order they are written.
But sometimes a step can tell you to move to a different step in the plan, instead of the next one.
And sometimes it can tell you to do different things if you see something different.
It can say "Go back to step 4" ... or "If the water is not hot yet, wait two minutes, then go back to step 3."
Here is a plan:
Here is another plan:
There is something funny about the second plan!
If we started following that plan, we would never stop.
We would just keep walking to the store, buying a food, and walking back home.
Forever.
(Or until we decide it is a dumb plan and we should stop following it.
But a computer couldn't do that.)
You may have heard songs like "The Song That Never Ends" or "Ninety-Nine Bottles of Drinks on the Wall".
Both of these songs are like plans.
When you are done singing a part of the song, you follow a plan step to get to the next part.
In "The Song That Never Ends", you just go back to the beginning.
But in "Ninety-Nine Bottles of Drinks on the Wall", you take one away from the number of bottles of drinks.
And if there are no more bottles, you stop!
But if there are more bottles, you sing the next part.
Even though it is a very long song, it does have an end.
(There is a bad joke about people who write plans for computers.
It is also a joke about hair soap.
There is a plan written on the hair soap bottle:
The person who writes plans for computers starts washing their hair and does not know when to stop!
Normal people know that "repeat" just means "do it a second time, then stop" and not "keep doing it forever". But in a computer plan, it would mean "do it forever".)
It is nice to know out how long a plan will take for us to do.
It is really nice to know if it is one of those plans that never ends.
If it is, then we could just say, "I won't follow this plan! It never ends! It is like that dumb song or the bad joke!"
The Halting Problem (Part Two)
Can we have plans for thinking about other plans? Yes, we can!
Suppose that we found a plan, and we did not know what kind of plan it is.
Maybe it is a plan for how to make a food.
Or maybe it is a plan for how to go by car to another city.
Or maybe it is a plan for how to build a house.
We don't know.
Can we have a plan for finding out?
Yes! Here is a plan for telling what kind of plan it is:
xkcd's Up-Goer Five comic gave technical specifications for the Saturn V rocket using only the 1,000 most common words in the English language.
This seemed to me and Briénne to be a really fun exercise, both for tabooing one's words and for communicating difficult concepts to laypeople. So why not make a game out of it? Pick any tough, important, or interesting argument or idea, and use this text editor to try to describe what you have in mind with extremely common words only.
This is challenging, so if you almost succeed and want to share your results, you can mark words where you had to cheat in *italics*. Bonus points if your explanation is actually useful for gaining a deeper understanding of the idea, or for teaching it, in the spirit of Gödel's Second Incompleteness Theorem Explained in Words of One Syllable.
As an example, here's my attempt to capture the five theses using only top-thousand words:
If you make a really strong computer and it is not very nice, you will not go to space today.
Other ideas to start with: agent, akrasia, Bayes' theorem, Bayesianism, CFAR, cognitive bias, consequentialism, deontology, effective altruism, Everett-style ('Many Worlds') interpretations of quantum mechanics, entropy, evolution, the Great Reductionist Thesis, halting problem, humanism, law of nature, LessWrong, logic, mathematics, the measurement problem, MIRI, Newcomb's problem, Newton's laws of motion, optimization, Pascal's wager, philosophy, preference, proof, rationality, religion, science, Shannon information, signaling, the simulation argument, singularity, sociopathy, the supernatural, superposition, time, timeless decision theory, transfinite numbers, Turing machine, utilitarianism, validity and soundness, virtue ethics, VNM-utility