The approach suggested by many researchers is based on universal physics-based constants that are the same in any numerical system. Properties of hydrogen are popular since our new friends should be very familiar with it. When hydrogen changes energy states it emits electromagnetic radiation with a wavelength of 21 cm/frequency of 1420 MHz. I have no idea how to represent that in the ED message system, but it's a signal SETI and others look for (a narrow band radio signal of 1420 MHz). The number "Pi" (3.14....) and "Phi" (golden ratio) are also possible options.
We have two possible routes to take in establishing relations with xenoforms:
1. Peace
2. The other thing
Let's admit it: A large portion of the galactic community want option 2. Option 2 is the easiest: See alien. Shoot alien.
Option #1 seems like it would be much harder but it really isn't. If we want to communicate that our intentions are peaceful then all we have to do is attempt to communicate. Any attempt to establish a dialog should be enough to communicate that we are a species that can be reasoned with. It doens't matter if the communication is succesfully understood at first. The mere act of attempting to communicate is, in it's own right, a form of communication.
Trying to establish communication in base-10 may be asking too much. The example cited by the OP could be interpreted too many ways. Binary is much more likely to be universally understood. Representing the Pythagoras theorem is also too complicated for the limited tools we have at our disposal.
The first thing we need to do is establish the fact that we want to communicate mathematically. I suggest we start with the following text strings:
We've now established that we are really clever and know some basic mathematical principles. We've also established that we really like the number 10. Nice but we really don't want to type dots all day. Let us teach them some binary:
They now know that a null quanity is reprezented by the symbol "0" and that the symbol "1" represents a quanitity. We've also established place values for our binary digits. We can move foward now by teaching them operands:
We've now established the rules for addition, subtraction, multiplication and division. Bravo us! We've also established the concept of 'not equal' or 'false' by giving them a division by zero error. We can now answer simple true or false questions with either '=' or '!'.
Now that we have our numbers established it is time to blow there minds! Point your ship to Merope and then enter in the distance to Merope in binary. Then point your ship to Sagittarius A* and type in the distance. DON'T give them the distance to Earth though! We don't want invite them over for tea just yet!
If you don't want to deal in binary you can hope that the aliens are particularly clever and skip directly to base-10. The principles are the same. Start with simple dots to represent a quantity and match that quantity to it's decimal equivalent:
Anyone remember that scene in bgs where the human was waiting to meet the cylons diplomatically in that station and what happened when they finally returned?
If it sounds like this http://www.sa-matra.net/sounds/babylon5/Shadow-Birth.wav
Then check several things
1. You've made a will
2. you're wering clean underpants (highly unlikely at this stage)
3. Always think how lucky you are that life has been good to you so far, however, if life has'nt been good to you so far given your current situation of about to die to alien laser cannon fire and then be eaten by things with tentacles for faces, consider how lucky you are that life wont be bothering you for much longer.
Bill
I'm organising a convoy to Beagle point.. leaves 5 minutes ago
First we give them the Fibonacci sequence, then we give them a truncated Fibonacci sequence, then we build them a model of the galaxy. But one thing we don't do is show them where we are located in the galaxy.
I suggest we throw some slaves out in front of them.
1. If they take the 'bait' we will know we are in trouble.
2. If they do nothing they will realise we are absolutely barbaric and not to be trifled with.
