# Another alien message, but from where?

"Alright everyone. After your great success decoding the stone tablet, we need your help with another message. We picked up a long sequence of radio activity and we're sure it's a message from aliens."

"However, we don't know who sent the message. That's where you come in. Your mission is this: decode the message and figure out where in the great wide universe this message came from. Good luck."

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Hint:

You don't need a telescope to see the star it came from.

• Would it be possible to break up the message for legibility? Rather than need to scroll forever just to see the whole thing? – dcfyj Feb 14 '17 at 17:13

Rejecting my previous answer as incorrect, the parameters determined by 2012rcampion are a close match for the Solar system (as in OUR solar system).

With the semi-major axis of Mercury (the first planet) of $70\times10^6$ km and that of the Earth (the third planet) of $150\times10^6$ km, the ratio is $2\frac{1}{7}$ precisely.

The radius of the Earth is $0.009145$ solar radii, which is practically $10^{-2}$ as expected.

Hence, the origin of the signal must be the Earth.

This is only the first step.

The message has 3589 symbols, either dots or dashes. These symbols can be arranged in a 37×97 grid, which looks promising:

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I've replaced the dashes with hash marks for clarity. (The message could also be represented a black-and-white pixel map.)

The top row ...

... looks like the definition of numbers and the sketches below make use of these numbers. The numbers are a bit pattern in a 2×3 block: The top two bits are always set to mark the glyph as a number. The middle row are the 1 and 2 bits, the bottom row are the 4 and 8 rows.

Although only the numbers from 0 to 11 are given, we can theoretically construct numbers from 0 to 15:

 0 ##   1 ##   2 ##   3 ##   4 ##   5 ##   6 ##   7 ##
#       #     ##            #       #     ##
#      #      #      #

8 ##   9 ##  10 ##  11 ##  12 ##  13 ##  14 ##  15 ##
#       #     ##            #       #     ##
#      #      #      #     ##     ##     ##     ##

The next block ...

... shows simple arithmetics. The three 1×3 glyphs are operators:

 + #    - #    * #    /      ^ #    = #
#      #      #      #
#                                  #
yielding the equations:
    1 + 2 = 3        5 - 4 = 1
6 + 4 = 10      11 + 11 = 0

2 * 3 = 6        4 / 2 = 2
4 * 3 = 12       6 / 2 = 3

3^2 = 9
2^3 = 8

The last sum 11 + 11 = 0 might suggest that either overflow isn't handled or that that the arithmetic is modular. (But modulo 22 would require more digit glyphs.)

The stuff to the right ...

... of the power equations probably has something to do with representation of rational numbers. The big 10×10 square is labelled 10 ^ 2.

• That was too quick guess. +1 I was thinking of it as Morse code -> Bacon Cipher(Binary) -> Text – Techidiot Feb 14 '17 at 17:31
• It looks like braille ... but I'm having issues with some of the letters. – Matt Feb 14 '17 at 17:47
• The first set of symbols appears to be the numbers 0 to 11 in this alien braille. – edderiofer Feb 14 '17 at 18:39

The message as an image, based on M Oehm's answer:

My interpretation:

* The top section counts up in binary numbers from 0 to 11. It's similar to the numbering system in the Arecibo message.
* The next six sections describe some mathematical operators. In order, they are addition, subtraction, multiplication, division, exponentiation, and fractions. There's a typo in the subtraction section, which has an equation that reads $11+11=0$ instead of $11-11=0$.
* The bottom section describes a solar system with four planets. The sun is 100 times more massive than the third planet (so the planet is likely a gas giant), and the ratio between the orbital radii of the first and third planets is $2\tfrac{1}{7}$.

• I can confirm that 11+11=0 is a typo. I'll fix it when I get home. Also, 100 is not mass. – qwertyu63 Feb 14 '17 at 21:59

Assuming that 2012rcampion correctly determined that $2\frac{1}{7}$ is the ratio of semi-major axes, I will propose my best guess of the system of origin for the signal:

Kepler-286 at R.A. 19h22m42s and Dec. +48°17'39''.

The system has 4 planets with the semi-major axes ratio of the third to the first one of $2.21$ (using Kepler's third law $\left (\frac{T_3}{T_1}\right )^2 = \left (\frac{R_3}{R_1}\right )^3$), which is reasonably close to $2\frac{1}{7}$. The ratio of the radius of the star to the radius of the planet is $10^{1.85 \pm 0.16}$, which is again consistent with the message.

This is the closest match I could find in the Exoplanet Archive.

My next best guesses would be Kepler-24 and Kepler-215.

• A good answer, but not the correct one. – qwertyu63 Feb 15 '17 at 15:05
• I just realized it: the parameters match our Solar system even closer. In fact, they're almost spot on. – Roman Feb 15 '17 at 15:13
• You're on to something. – qwertyu63 Feb 15 '17 at 15:16

This is a canonical answer to explain everything in the message. This explains the fixed version. The fixed errors are as follows:

Replaced 11+11=0 with 11-11=0.
Replaced 9/3=[1/3] with 3/9=[1/3].

Step 1: Finding the image.

There are 3589 characters in the message. 3589 is a semi-prime number (37x97). This means if you try to arrange them in a grid, there are only two ways to do it evenly. As it happens, the message starts with 37 dashes in a row.

By arranging the message like that, you can see a pattern emerge. This pattern can also be shown as a black and white image (dashes are black pixels, dots white pixels), as follows (scaled up 500%):

Step 2: Decoding the message.

At the very top of the message is a sequence of 12 2x3 symbols. These symbols are the numbers 0 through 11, as shown by the bars below them.
Each number symbol has the top two blocks filled in. From there the remaining blocks count the value of the symbol in binary starting at the top left, as follows:

 ##
12
48
Below the numbers are some equations, using the following 1x3 symbols:
 +  -  *  /  ^  =
#  #        #  #
#  #  #  #
#     #        #  
The actual equations are as follows:
 1+2=3   5-4=1
6+4=10  11-11=0

2*3=6   4/2=2
4*3=12  6/2=3

3^2=9
2^3=8
To the right of the exponents are fractions. A fraction is shown as a large bar over a division problem. I will put brackets around them in this explanation. The problems are as follows:
 1/2=[1/2]
3/9=[1/3]
4*[1/2]=2

Step 3: The diagram and the final reveal.

Below all of the math is a diagram of a star system. Four planets are shown in the system, as is the star.

The star is marked 10^2, or 100; the third planet is marked 1.

Some distances are labeled as well. The distance from the star to the closest planet is marked 1, while the distance to the third planet is marked 2+[1/7].

At this point, looking at the numbers reveals that the depicted star system is the Solar System (as in where Earth is).

The ratio of the Sun's radius to the Earth's radius is ~100.
The ratio of Mercury's orbit to the Earth's orbit is ~2+[1/7].

As Earth is in both equations and is known to contain life, it is apparent that the message came from Earth.