# If I had an alien race, how would they interpret our numerical characters as being numbers?

So say we discovered aliens through a wormhole near Saturn (Interstellar anyone?). Congratz to us! But we have a bigger issue in trying to communicate with them.

They developed in a completely different way than us, but their general physiology is the same (Bi-pedal humanoids that utilize vocal chords to speak). Assuming it takes hundreds of years for them to get information, how do we communicate?

After thinking about what everyone said about "Well we could communicate with math?" and "Math is universal." it raised the question of how would they recognize all of our current mathematical symbols even if they were to be included? (For example, what if they used a base 4 for their math rather than 10 or their characters are completely different?)

• You may also be interested in the movie "Contact", based on the book with the same title by Carl Sagan. Even the movie has a scene that very specifically discusses how to bootstrap scientific communication (specifically mathematics) in a one-way communication scenario. The book has more details, like how to give quantities and proportions of basic chemical elements, essentially showing how one might bootstrap not just mathematical and scientific but also engineering communications, in a quite plausible manner. – a CVn Jan 29 '16 at 21:15
• Also, since you appear to be new to the network, I want to point out that it's often better to wait a day or two before accepting an answer. When, and whether, to accept an answer is of course entirely up to you, but a question having an accepted answer often leads to it drawing less attention from the community, which in turn reduces the probability of it receiving further answers. Since the first answer(s) posted are far from always necessarily the best, waiting at least 24 hours (to allow people from different parts of the world to chime in) before accepting one is often adviced. – a CVn Jan 29 '16 at 21:20
• The first answer accurately and acutely answered my question, so I gave it the vote. From what I know, further discussion is for chat correct? – Anoplexian Jan 29 '16 at 22:44

This question has already been debated by exo-astronomers. The best answer they could come up with (using 1974 technology) was the Arecibo Message.

The details might change, but the essential idea is that in the first part of your message, you teach the aliens, "this is how we count."

0
1 .
2 ..
3 ...
4 ....
5 .....
6 ......
7 .......
8 ........
9 .........
10 ..........

11 ..........    .
12 ..........    ..

20 ..........
..........
21 ..........    .
..........

100 (*snip* a 10x10 grid of dots)


Then build communication from there. In the case of Arecibo, they used a binary system instead of decimal. If the aliens wrote back in their base four, we might expect:

X
A .
B ..
C ...
AX ....
AA ....    .


etc.

• This is probably the most plausible way it would happen, at least if the intent is exchange of information (that not being just an accidental side-effect). It has the benefit that it completely removes the dependence on the specific symbols used, which is a great thing when there is every reason to assume that the writing systems used would have absolutely nothing in common! – a CVn Jan 29 '16 at 21:14

The answer is "we'd do the best we can." No method of teaching language has a perfect 100% success rate.

One common approach that has been suggested in the past is to encode sequences which are very unlikely to occur by chance. For example, there are very few physical processes which can emit a stream of prime numbers, one after another. The idea is that the other species will try many different interpretations of the data, but hopefully the "right" meaning will stand out from the others.

What defines a "good" sequence" is a subject of much debate. This approach is dependent on the other species also finding a sequence meaningful. Some things, such as the series of prime numbers, are thought to be sufficiently fundamental to mathematics that we have a hard time considering languages where they are not given special status. Prime numbers have their roots in Peano arithmetic, which is remarkably fundamental. In fact, they are so fundamental that your particular concern of different bases is not an issue. 13 is a prime number. If they happen to use binary, 1101 is the same prime number. We will encode them differently, of course, but a series of numbers like this is a powerful tool for helping the other side understand the way we think.

Just brainstorming for fun, I could see sending .. ... ..... ....... ........... ............. on one frequency, with a corresponding decimal or binary sequence on a different frequency (in binary, it might look like -. -- -.- --- -.-- --.-, using a coding scheme with 2 symbols plus a space symbol). Provide enough correlatable data, and it becomes harder and harder for the aliens to misinterpret the meaning, because false hypotheses get weeded out.

I think anyone advanced enough to communicate with us through those means would posses some pretty advanced tech.

A computer analyzing the patterns in the messages would reach the conclusion that it's dealing with a mathematical algorithm, and they would just go from there.

I'm not saying it would be easy, but it's basically inevitable if both species are set on communicating with one another.

• That still doesn't accept the fact that their computers probably developed differently. Instead of binary, what if they were tri-nary instead? – Anoplexian Jan 29 '16 at 20:57
• @Anoplexian - a pattern is a pattern, is a pattern, is a pattern. – AndreiROM Jan 29 '16 at 20:59

Related to the Arecibo Message: the Golden Record sent out with the Voyager probes communicated the RPM necessary to play the record by expressing the fundamental transition of the hydrogen atom in binary. You could imagine using some constant like this, believed to exist far outside the Earth, as the basis for some kind of number system.

• In that case, there's tons of parallels, but that would require them knowing what the actual binary code was and that they'd recognize it as being binary, rather than the. I'm talking about a fundamental difference between the races. That also requires them to correctly decipher the message, which could result in false decoding messages. – Anoplexian Jan 29 '16 at 22:33

You would need to create a Rosetta Stone of sorts. Also, look at examples of here on earth where separate human cultures contacted each other for the first time. You need to pick a universal constant that any advance species would be familiar with, then use that as a template of sorts to explore our language. https://en.wikipedia.org/wiki/Pioneer_plaque This may give you some good ideas from people who have gone before us on this topic and also help you understand what I am saying.