Just One Sentence

If this is to be taken as a sort of prophetic/religious statement that will certainly be believed, how about this:

"It is better to rely on the labour of machines than the labour of beasts, and better to rely on the labour of beasts than the labour of man".

(Based on the idea that historically, technological progress was often disincentivized by the abundance of cheap/slave labour).

"If you perform experiments to determine the physical laws of our universe, you will learn how to make powerful weapons."

It's all about incentives.

"Most diseases are caused by tiny little mindless creatures the reproduce and spread quickly and live in sick people's bodies, and quite a few of them can be killed be a certain mold that you can grow on bread."

Hmm, how many "and's" can I put in this one sentence? This reminds me of a competition for extra credit in one of my CS classes to write a C++ program in "as few statements as possible," where I took the obvious algorithm, completely unrolled the loop, and used logical connectives to stick every statement together into one. I skipped class the day the winner was announced, and the teacher later said he changed the rules and let the class vote for a winner, which wasn't me.

"The use of semicolons will enable you to construct arbitrarily long sentences".

No, seriously. To reconstruct physics, how about "Use inclined planes to slow down motion; this will enable you to make careful measurements". That's how Galileo got started.

Future creatures, you must find ancient human DNA and revive us, or you will suffer a second apocalypse.

If we're talking about knowledge the ancients could immediately use, why bother with physics or macroeconomics? "There are tiny creatures too small to see that spread between living things, and make you sick if too many get into you, but there are ways to kill them" seems a lot more practical.

Given the fuzziness, I'll just take it as an exercise in wit:

• "LOCKSS: Lots Of Copies Keep Stuff Safe." They'll figure out the science. But we lost all scientific knowledge, I don't want that to happen twice.

• "Rub dry wood until it makes like sun." Hopefully the taste of good steak will get them going.

Before constructing the answer, it's usually good to clarify the problem. First, it's probably good to re-frame it in terms of past and present, not the (unknown) future. For example, assuming there were an extinct civilization 100,000 years ago which managed to pass that one sentence on, what bit of wisdom to the ancient Greeks/Babylonians/Etruscans/... would you expect to be most useful? How and why? What does it mean to be useful, anyway? Useful to whom? To them? To us?

Did they come up with that bit of wisdom by themselves and rejected or ignored it, anyway? Would it have been different if it was unearthed as a relic of a past civilization?

Even though innovation, trade and competition in labor, product and capital markets can sometimes harm individual businesses and workers, restricting these forces almost always reduces the total prosperity of a society.

"The world is not made of things with minds, but of small mindless things that obey regular patterns."

As far as major scientific facts go, I am surprised that evolution has yet to be mentioned. Let me try:

"All the complexity of Life on Earth comes from a single origin by the following process: organisms carry the plan to reproduce and make copies of themselves, this plan changes slightly and randomly over time, and the modified plans which lead to better survival and reproduction tend to outcompete the others and to become dominant."

What does it mean to send "one sentence" to the future? Does the future understand English? How precise of a concept can we give them?

Typically, I interpret that as "what concept would you like people to have instinctually?", which most people respond to with "here's something that I wished my contemporaries understood, and so I'm going to inflict it on imaginary future post-apocalyptic humans," apparently because they haven't suffered enough.

When was the atomic hypothesis confirmed? If I recall correctly, it was only when chemists started noticing that the outputs of chemical reactions tended to factorize a certain way, which is to say that it took millennia after Democritus to get the point where the atomic hypothesis started making clearly relevant experimental predictions.

Mmm. I don't think it's that terrible, but it does appear designed to put people at Alhacen's level on the right track, rather than to put people at Aristotle's level on the right track. For example, I seem to recall the correct understanding of heat being held up by the atomic hypothesis not being widely accepted; if you know that atoms exist, then calculating everything correctly is fairly straightforward- but you do need some math to get it right. Feynman misses the opportunity to hint at electricity except very obliquely.

"Stop trying to sound wise and come up with theories that make precise predictions about things you can measure in numbers."

Why start off with the negative? Galileo's quote seems to capture the same idea more positively:

Measure what is measurable, and make measurable what is not so.

As for macroeconomics, money is useful, but only insofar as it facilitates trade. My first try would be:

Human skill accumulates because of specialization, returns to specialization are capped by the size of the market; trade increases wealth by allowing greater specialization which allows greater skill.

If they can understand English, perhaps they can understand math, the supposedly universal language. With that in mind, here is a single equation by Sean Carrol that completely describes the fundamental physics of what he calls "everyday life on Earth".

In general, I'd expect sentences that convey information about the scientific process to be much superior to sentences that contain merely some clever concoction of facts. Analogous to teaching a man to fish versus just giving him some fish he would have caught anyways given the right method. The only exception would be information that is extremely unlikely to be experimentally discovered* (yet the previous generation stumbled upon) but the expected value of which would outweigh some optimization of the scientific method. (*Before a cataclysm)

Come to think of it, the most such important piece of information (and also keeping with the hypothetical) would be information about the cataclysm (only applies for anthropogenic cataclysms). The reason is that ceteris paribus, a similar pattern (which we would even help along with our usual sentences) could well lead to a similar outcome (another catacylsm). Gotta break the circle.

Alternatively, what about "ALL THESE WORLDS ARE YOURS EXCEPT EUROPA ATTEMPT NO LANDING THERE". Imparts some important cultural information. Hope the poor blokes don't take it too literal and implement a naval embargo of Europe.

Thou shalt not make pipes out of lead, for God hates that.

I'd be thinking along the lines of "keep heating different rocks up a lot, you'll eventually get really useful stuff for building things out."

This is assuming we get fire pretty easily (so we don't have to transmit that knowledge) but reflecting the millenia before our tech included metal.

Wow, I'm missing the more important surplus: "find the plants you can eat and figure out how to grow them yourself in one place."

I'm not enough of a prehistorian to know which came first: metal or agriculture. My principle in choosing one of these is to skip thousands of years of a low level of subsistence, of pushing tech ahead by thousands of years by concentrating our successors in an area of great value.

My theory is that economic surplus will produce science and knowledge more surely than anything we can ever communicate to our successors. Best get them jumpstarted on producing.

The map is not the territory, but if you keep paying attention and checking, you can improve the map.

What's wrong with admitting you can't produce such sentence? Note, I'm not saying there isn't one, Kolmogorov complexity and all, only that chances are extremely low that any human now can produce it.

As for Feynman statement, yeah, it's wrong if you read it literally (I read it as "I can't emphasize enough how important this following fact is") , but Eliezer (and all commenters I read) made the same mistake really - he produced the sentence he thought would help them most, not one that would "contain most information in the fewest words".

If we want to produce a sentence of highest compression, they probably won't be able to read it for ages, so what's the point. If we want to produce a sentence that would help them most I have no idea what should it be. Maybe some math, maybe physics, maybe agriculture or economics. Depends on the cataclysm too. Either way, I have no idea. I think the only thing the answers given so far convey is biases in people giving them ;-)

"Consider it both a threat and an opportunity that smarter-than-human beings can probably be created using machines that can do lots of calculations really fast."

Never attribute to malice what can be explained by stupidity.

If I recall correctly, it was only when chemists started noticing that the outputs of chemical reactions tended to factorize a certain way, which is to say that it took millennia after Democritus to get the point where the atomic hypothesis started making clearly relevant experimental predictions.

IIRC, even then, plenty of people considered it somewhat speculative, and it didn't become universally accepted until Einstein's explanation of Brownian motion.

An intuitive, one sentence explanation of the scientific method. Come to think of it this might be handy in general. Eliezer's is already pretty good.

I wondered what Feynman was thinking, so I looked up the context. Here is an excerpt and a longer .doc. Google books. But it didn't help.

"The new basic principle is that in order to learn to avoid making mistakes we must learn from our mistakes." – Karl Popper, In Search of a Better World.

"It is an attitude which does not lightly give up hope that by such means as argument and careful observation, people may reach some kind of agreement on many problems of importance; and that, even where their demands and their interests clash, it is often possible to argue about the various demands and proposals, and to reach – perhaps by arbitration – a compromise which, because of its equity, is acceptable to most, if not to all." - Karl Popper, The Open Society and Its Enemies Volume 2.

I'd let you pick one or the other of these sentences, and be fine with either choice.

"Stop trying to sound wise and come up with theories that make precise predictions about things you can measure in numbers."

It seems a bit anthropocentric to assume that the next gang of creatures will also be interested in "sounding wise". Edit: Unless they're humans, of course.

Math:

"Use your intuition to guide you, but try whenever there's any doubt over what is correct to state what you mean in a rigorous form going back to axioms."

Does this involve too many implicitly defined terms?

Can I use Rule 110 as an extensional definition pointing to what is arguably the central insight of computation? "Rigorously analyze the relationship between the consequential patterns and initial conditions if, for each row of black and white stones, the next row is arranged such that a black stone is placed beneath a white stone if the stone to the right of the white stone is black, a white stone is placed beneath a black stone if the stones to either side of the black stone are also black, and a stone of the same color is placed beneath the stone in the preceding row otherwise."

I suppose something like:

Competition and creation, the former stopping the insane forms of the latter, are responsible for pretty much everything you see, and, if you foster them in your society, can - eventually - give you more than you can possibly imagine.

In my discipline? I guess

Write code that's easy to update without breaking dependent code.

That'll save the ancient programmers of the 1950's some time.

If I were trying to build up programming from scratch, it'd get pretty hairy.

Build a machine that, when "x = 1.1; while (10. - x*x > .0001) x = x - ((x * x - 10.) / (10.*x)); display x" is entered into it, displays a value close to the ratio of the longest side of a right triangle to another side expressed as the sum of 0 or 1 times the lengths of successive bisections.

Math:

"Write down numbers by using ten symbols called digits for the numbers zero through nine, and writing XY, where X is a number and Y a digit, for the number equal to ten times the number represented by X, plus the number represented by Y."

Maybe this could be optimized by picking a better base to work in (2? 8? 12?), but if post-apocalyptic humans have the same number of fingers, then base 10 has its advantages as well.

"Your dirty lying teachers use only the midnight to midnight 1 day (ignoring 3 other days) Time to not foul (already wrong) bible time."

deleted

"Rub dry wood fast until it makes like sun."

How many semicolons are we permitted?

More seriously:

"Study processes whose inputs are also their outputs."

"You are not special. You are not a beautiful or unique snowflake. You're the same decaying organic matter as everything else. " -http://www.imdb.com/title/tt0137523/quotes

(Not actually)

Prosperity depends on trust, especially trust that the fruits of one's labour won't be arbitrarily taken away; therefore there should be clear and reliable property rights.

For all X, either X xor not(X) holds, now start deriving things.

Political disputes are usually terminal value disputes, and pretending otherwise leads to confusion of facts and preferences.

Alternatively, something about hidden complexity of wishes and its relevance to defining legal and moral obligations.