The Up-Goer Five Game: Explaining hard ideas with simple words

Rob Bensinger

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:

Intelligence explosion: If we make a computer that is good at doing hard things in lots of different situations without using much stuff up, it may be able to help us build better computers. Since computers are faster than humans, pretty soon the computer would probably be doing most of the work of making new and better computers. We would have a hard time controlling or understanding what was happening as the new computers got faster and grew more and more parts. By the time these computers ran out of ways to quickly and easily make better computers, the best computers would have already become much much better than humans at controlling what happens.
Orthogonality: Different computers, and different minds as a whole, can want very different things. They can want things that are very good for humans, or very bad, or anything in between. We can be pretty sure that strong computers won't think like humans, and most possible computers won't try to change the world in the way a human would.
Convergent instrumental goals: Although most possible minds want different things, they need a lot of the same things to get what they want. A computer and a human might want things that in the long run have nothing to do with each other, but have to fight for the same share of stuff first to get those different things.
Complexity of value: It would take a huge number of parts, all put together in just the right way, to build a computer that does all the things humans want it to (and none of the things humans don't want it to).
Fragility of value: If we get a few of those parts a little bit wrong, the computer will probably make only bad things happen from then on. We need almost everything we want to happen, or we won't have any fun.

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

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.

As an example, here's my attempt to capture the five theses using only top-thousand words:

Intelligence explosion: If we make a computer that is good at doing hard things in lots of different situations without using much stuff up, it may be able to help us build better computers. Since computers are faster than humans, pretty soon the computer would probably be doing most of the work of making new and better computers. We would have a hard time controlling or understanding what was happening as the new computers got faster and grew more and more parts. By the time these computers ran out of ways to quickly and easily make better computers, the best computers would have already become much much better than humans at controlling what happens.
Orthogonality: Different computers, and different minds as a whole, can want very different things. They can want things that are very good for humans, or very bad, or anything in between. We can be pretty sure that strong computers won't think like humans, and most possible computers won't try to change the world in the way a human would.
Convergent instrumental goals: Although most possible minds want different things, they need a lot of the same things to get what they want. A computer and a human might want things that in the long run have nothing to do with each other, but have to fight for the same share of stuff first to get those different things.
Complexity of value: It would take a huge number of parts, all put together in just the right way, to build a computer that does all the things humans want it to (and none of the things humans don't want it to).
Fragility of value: If we get a few of those parts a little bit wrong, the computer will probably make only bad things happen from then on. We need almost everything we want to happen, or we won't have any fun.

If you make a really strong computer and it is not very nice, you will not go to space today.

Complex numbers

I don't know why that one caught my eye, but here I go.

You've probably seen the number line before, a straight line from left to right (or right to left, if you like) with a point on the line for every real number. A real number, before you ask, is just that: real. You can see it in the world. If I point to a finger on my hand and ask, "how many of these do I have?", the answer is a real number. So is the answer to "how tall am I?", and the answer to "How much money do I have?" The answer to that last question, notice, might be less than nothing but it would still be real for all that.

Alright, what if you have a number line on a piece of paper, and then turn the paper around by half of half a turn, so the number line has to run from top to bottom instead of left to right? It's still a number line, of course. But now you can draw another number line from left to right, so that it will go over the first line. Then you have not one line but two.

What if you next put a point on the paper? Because there is not one number line but two, the point can mean not just one real number but two. You can read off the first from the left-to-right line, and then a second from the top-to-bottom line. And here is a funny thing: since you still have just one point on the paper, you still have one number — at the very same time that you have two!

I recognize that this may confuse. What's the deal? The thing to see is that the one-number-that-is-really-two is a new kind of number. It is not a real number! It's a different kind of number which I'll call a complete number. (That's not the name other people use, but it is not much different and will have to do.) So there is no problem here, because a complete number is a different kind of number to a real number. A complete number is like a pair of jeans with a left leg and a right leg; each leg is a real number, and the two together make up a pair.

Why go to all this trouble for a complete number that isn't even real? Well, sometimes when you ask a question about a real number, the answer to the question is a complete number, even if you might expect the answer to be a real number. You can get angry and shout that you don't want an answer that's complete, and that you only want to work with a number if it's real, but then you'll find many a question you just can't answer. But you can answer them all if you're cool with an answer that's complete!

For what it's worth, I dislike the term "real number" precisely because it suggests that there's something particularly real about them. Real numbers have a consistent and unambiguous mathematical definition; so do complex numbers. Real numbers show up in the real world; so do complex numbers. If I were to tell someone about real numbers, I would immediately mention that there's nothing that makes them any more real or fake than any other kind of number.

Unrelatedly, my favorite mathematical definition (the one that I enjoy the most, not the one I... (read more)

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The Up-Goer Five Game: Explaining hard ideas with simple words

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The Up-Goer Five Game: Explaining hard ideas with simple words

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