Convincing ET of our rationality
Allow me to propose a thought experiment. Suppose you, and you alone, were to make first contact with an alien species. Since your survival and the survival of the entire human race may depend on the extraterrestrials recognizing you as a member of a rational species, how would you convey your knowledge of mathematics, logic, and the scientific method to them using only your personal knowledge and whatever tools you might reasonably have on your person on an average day?
When I thought of this question, the two methods that immediately came to mind were the Pythagorean Theorem and prime number sequences. For instance, I could draw a rough right triangle and label one side with three dots, the other with four, and the hypotenuse with five. However, I realized that these are fairly primitive maths. After all, the ancient Greeks knew of them, and yet had no concept of the scientific method. Would these likely be sufficient, and if not what would be? Could you make a rough sketch of the first few atoms on the periodic table or other such universal phenomena so that it would be generally recognizable? Could you convey a proof of rationality in a manner that even aliens who cannot hear human vocalizations, or see in a completely different part of the EM spectrum? Is it even in principle possible to express rationality without a common linguistic grounding?
In other words, what is the most rational thought you could convey without the benefit of common language, culture, psychology, or biology, and how would you do it?
Bonus point: Could you convey Bayes’ theorem to said ET?
I’m reminded of the hoary old anecdote about the primate intelligence researchers who put a chimpanzee in a room with a collection of intelligence-testing toys to see what it would do, and when they peek through the keyhole all they see is a chimpanzee eye watching them.
Which is to say, I doubt that my primary goal in this situation would be to convince them of my rationality, but rather to learn as much about them as I could.
That said… no, I don’t think I could communicate much of anything reliable without the benefit of common language, culture, psychology, or biology.
Funny story, but it raises a good point. Perhaps an expression of curiosity would be enough to convince them of our worthiness.
On the other hand, that doesn’t seem to have convinced us about the chimpanzees.
For what it’s worth, the chimps have me convinced.
Show the ET my cellphone?
More seriously: draw a rough map of the Earth showing my location, and then a diagram of the Solar System with approximately correct distance ratios. An irrational species isn’t likely to have such information. See Terry Tao’s presentation The Cosmic Distance Ladder for some epic applications of rationality to measuring large distances.
Amazing, thanks for the link. This is what most interests me—not what we know in science, but how we know it, when classes tend to focus on the former. (Asimov’s book Atom is an excellent answer to the question of how we got to our current atomic models.)
Great link. It reminds me of my freshman astronomy lab which actually had us students calculate for instance the diameter and mass of the Earth and sun, and through the semester moved up to the level of using parallax and blackbody spectra to calculate distance to various stars.
This is kind of an unfair question if you’re cut off from the internet. We’re a technological civilization, we’ve realized our wet brains are inadequate for storing all our knowledge so we put most of it on silicon where we can access it if we need it. It isn’t really fair to expect us to demonstrate our rationality without giving us access to the primary repository of our knowledge.
BUT:
It should be pretty easy to explain our formalization for the real number system and propositional logic.
|+||=|||
1+2=3
||+||=||||
2+2=4
| : 1
1+1=2
+1=3
+1=4
+1=5… and so on
1+1=3 :: F
1+1=2 :: T
Then give truth tables for elementary logical connectors. This probably only works if they have some kind of analogous formalization for math, but if they’re building and flying spaceships instinctively- instead of doing the math … well, first damn. Second, there isn’t any kind of symbolic proof of rationality you could give, but if they want to know if you are they’ll probably want to see how you play games and will test you themselves.
You could then give a written description of updating by the conditionality principle. But I’m not sure you could express the significance of that exactly.
Then you could draw a periodic table- though I probably couldn’t do it from memory. You could relate the elements to elements in the solar system by labeling the bodies with the proportions of the major elements found in the sun and on each planet.
Do physical observations determine our visual models for atoms with a sufficient degree of specificity for this to work?
Depending on how much of the periodic table you have memorized you could go a little further with decimal notation to give atomic number, atomic weights, and specialized symbols.
H, 1, 1.01
He, 2, 4.00
Li, 3, 6.94
Be, 4, 9.01
B, 5, 10.8
C, 6, 12.01
Past that point you can probably just get away with reference by atomic number and you only have to have the periodic table’s order memorized (...boron, carbon, nitrogen, oxygen, fluorine, neon, sodium, magnesium, etc). Then you can diagram basic molecules like water as “(1)-(8)-(1)”. Nail down the meaning by spitting for a demonstration of “liquid”, and maybe come up with a convention for angles and show the angle between the two hydrogen dangling off the oxygen being ~104.5 degrees. Ask for 80% gaseous “(7)-(7)” and 20% gaseous “(8)-(8)” plus water to explain your biological requirements for a few days. Diagram glucose, fatty acids, salt, and essential amino acids so they can fabricate enough food to last until scurvy or some other nutrient deficiency kicks in.
That should give enough time for them to decompile our genome and learn English if the aliens are any good at being our technological superiors :-)
While waiting for that, constellations might also be a good place to go, if you have access to the night sky or a portal in their ship or something? The apparent movement of stellar objects can serve as a chronometer (if you can still see the sun or the moon or something). Once you’ve got a stable unit of time and a stable unit of distance you can start talking about stars by pointing and describing light years. If I remember correctly, Vega is around 28 light years away, Betelgeuse is about 600. (Google says… 25 and 646.) Then you can ask “How far have you traveled to get here?”
You should be able to get time just by labeling the orbits in your diagram of the solar system. Of course, you’ll have to remember that the sidereal year is one day longer. Just label the Earth’s orbit “year” and the Earth’s spin “sidereal” and then write 1(year)=366.25 days. Hopefully the aliens are tolerant of approximations. They may first think these are distances, but their next guess when they see the math doesn’t work would probably be time.
Then draw a line on your diagram between the Earth and the sun. Thats 1AU. The speed of light is about 173 AU/day (it’s a little less with sidereal days, a little more with solar days).
The problem then is that all the constants you’re used to are based the solar day. Eventually the aliens will get confused. One solar day = 1.00273791 sidereal days. But no one will remember that. It might be easier to remember 1 sidereal day is 23 hours 56 minutes and 4 seconds.
Or I guess if you have a constellation chart your could draw in the ecliptic plane and label that. But dang are our units screwed up.
1AU =149 598 000 kilometers but if you’re a provincial American like me you know miles. 1AU=92 955 887.6 miles…
I don’t think a lot of scientists have this stuff memorized (1 obviously looked up just about all these numbers, except for hrs/sidereal day).
I would be really nice if we had all our units based off the speed of light or something. That would make this so much easier.
Our sample size of intelligent species is pretty small. We don’t have any good reason to think that they would prefer “rational” entities or would even have a notion of “rational.” One could easily construct other hypotheticals, like an alien species that was intensely religious and considers signs of rationality to be bad (there are humans who do just fine in careers like engineering and claim to have such viewpoints, so the idea of a species reaching high tech levels and having such hang-ups isn’t implausible.)
True, but would you agree that it is more likely that rational entities attain spaceflight capabilities? Also, rationality is likely to share some universals, whereas religion seems far less likely to.
I think most religions require some belief without (and possibly in spite of) evidence, or using words which are almost meaningless.
It would be interesting though to see if aliens find different contortions on which to base religious beliefs. Like, a stable equilibrium of people pretending to see what their religion asserts and avoiding signalling otherwise Emperor’s New Clothes style or something.
That occurs in some human religions also just less commonly with sight but rather other observational claims. For example, in some forms of Protestant evangelicalism it is uncommon for people to talk about all the terrible things they did before they accepted Jesus as their personal lord and savior. Very few of those people were the drug-fueled, alcoholic, decadent, Satan-worshippers that they claim to have been. But no one calls them out on it.
Since somebody already laid out the groundwork for situations like these, I guess I would start with that.
Once they know our numbers, we can hopefully start defining operations like addition, multiplication, and exponentiation, then move on to algebra and calculus. Great, so now they know we know some math. To show them we know science, regurgitating scientific knowledge might work, but I think they would be slightly more impressed with a prediction that utilizes that knowledge, followed by observation and confirmation. The number of seconds it takes an object to fall from a given height, calculated beforehand and then measured, or the number of days until some celestial phenomenon, represented by, for example, making a pile of pebbles for each unit of time you expect the event to take and taking away one pebble at each interval (expecting the punchline to occur at no pebbles), would be worth considering as attempts.
I love that link. It reminds me of a poster I once saw which gave instructions on how to make electric generators, fixed wing aircraft, penicillin, and the like for prospective time travelers.
I own that poster in t-shirt form. (The original is here.)
Oh yeah, this one. They are so similar that I can only conclude that they were either made by the same person, or someone is copying someone.
Great link. It reminds me of my freshman astronomy lab which actually had us students calculate for instance the diameter and mass of the Earth and sun, and through the semester moved up to the level of using parallax and blackbody spectra to calculate distance to various stars.
Hans Freudenthal wrote a book “Lincos: Design of a Language for Cosmic Intercourse, Part 1”) in which he shows how to build up communication with aliens over nothing but a radio channel that can transmit pulses. He starts with mathematics and logic, and builds up to other concepts such as time, space, and social interaction. Part 2 would have taken it further but never appeared.
However, as far as I know it has never been used to establish communication with aliens.
I suppose I might try potential diagrams, maybe draw a harmonic oscillator potential and eigenfunctions. That’s really just playing to my strengths, though, not seeking something that would be best understood.
The pythagorean theorem is probably the best way. It’s so ridiculously fundamental, and there are some excellent pictoral proofs that require no language and demonstrate rationality quite well.
How would the aliens even know what these were?
Well, if they had eyes they could probably figure it out pretty quickly. If I saw someone representing them by colors or something I’d probably catch on. I’d be willing to wager that representing lines in space by other lines on surfaces is pretty universal, if you’re worried about the graph-like part.
Writing prime numbers in dots is one idea; drawing a rough diagram of the solar system is another. Or if the primary goal is to prove that humans are sentient, civilized and therefore “people”, I’d just show them my various gadgets: cell phone, iPod, Kindle, calculator, etc.
Pre-scientific societies have managed to build quite complex machinery. For instance the Antikythera mechanism, Roman textile mills, Egyptian irrigation systems, etc. Is it possible aliens could develop something as complex as a calculator without first attaining scientific literacy? If so electronics wouldn’t necessarily prove scientific literacy to them.
Good luck figuring out how to make microchips without at least some scientific knowledge. Even if it could be done, the probability does not seem very high to me.
Send them a bunch of prime numbers?
Throughout most of human history, most people knew pretty much nothing about math, logic, or science. Could they convey that they are rational? Should they fail this test?
A related question:
What’s the most rational thought you could convey without the benefit of common language, culture, psychology, biology, or modern knowledge?
Or
How do you convey that you could become rational?
With that kind of constraint, you may well be doomed. Curiosity, as in the chimpanzee story, might be your best bet.