Interstellar Message

 

Interstellar Message: Page #7

Parameter

Value

Date/Time Began 04/22/2007 12:41:49 UT
Number of Times Repeated 1,024
Date/Time Finished 04/27/2007 06:24:23 UT
Number of Pulses 494
Page Duration (With Delay) 6 min 39.76 sec
Data Transfer Rate 3.71 bits per second
Symbol A (84.7 Hz) Occurs 32 times
Symbol C (119.8 Hz) Occurs 144 times
Symbol D (142.4 Hz) Occurs 168 times
Symbol E (169.4 Hz) Occurs 32 times
Symbol F (201.5 Hz) Occurs 48 times
Symbol I (338.8 Hz) Occurs 9 times
Symbol L (569.8 Hz) Occurs 29 times
Symbol M (677.6 Hz) Occurs 32 times

 

Page #7 is as follows:

1.) DDFCDMDCCDEA
2.) DDDFCDMDCCCDDEA
3.) CCCDFCDMCCCCCCDEA
4.) DLCDFCDMDCLCDDEA
5.) CDFDDMCCCDEA
6.) DDFDDMDDCDDEA
7.) DCDFDDMDCDDDDDEA
8.) DLDFDDMDDCLDDEA
9.) DCCDFDDIFCDMEA
10.) CCCCDFCCDIFCDMEA
11.) DCCDDFDCDIFCDMEA
12.) DCLCDDFDLCDIFCDMEA
13.) CCCDIFCDIFDDMEA
14.) CFCFCDMEA
15.) DFDFDDMEA
16.) DFDDFCMEA
17.) DCCDFDLCMDDEA
18.) DCCCDDFDLCMDDDEA
19.) CCCCCCDFDLCMCCCDEA
20.) DCLCDDFDLCMDLCDEA
21.) DDCDDFDCDCDCDCLCMDDEA
22.) CCCCDFDCLCMCDEA
23.) CCCCDFDDLCMCCCDEA
24.) DCCCLDCDFDCLCMDLDEA
25.) CDDFCCCDDCDDFDCDCDCDCLCMEA
26.) CFCFDLCMEA
27.) DFDFDCLCMEA
28.) DLDDDFDLDDDFDMEA
29.) DCCLCFCCCDFDIMEA
30.) DCCCLCFCCDFCDIMEA
31.) DCLCFCCCCDFDLICMEA
32.) DDDCCDCDDCLDFCDFDLCMEA

Translation Notes

The symbol M is the only new symbol but it occurs exactly once on each line.  Taking line #1 we have DD followed by F followed by CD followed by M followed by DCCD followed by E.  We can translate this as:

3, 2 M 9 =    or    3 M 2 = 9

Clearly the symbol M represents raising to a power.  Lines #14 and #26 demonstrate that zero raised to any power equals zero.  Lines #15 and #27 demonstrate that one raised to any power equals one.  Line #16 demonstrates that any nonzero number raised to the power of zero equals one.  Line #28 demonstrates that any nonzero number raised to the power of one equals itself.  Line #32 equates the square root of two with DDDCCDCDDCLD which is 1.0110100111 binary (i.e., 1.413 decimal).  Note that the square root of two is an irrational number which requires an infinite number of digits to represent it with complete accuracy.  We represent it as a binary number with ten binary digits after the binary point which is only an approximation.  The complete English translation of page #7 is as follows:

  1.) 3 ^ 2 = 9
  2.) 7 ^ 2 = 49
  3.) 8 ^ 2 = 64
  4.) 2.5 ^ 2 = 6.25
  5.) 2 ^ 3 = 8
  6.) 3 ^ 3 = 27
  7.) 5 ^ 3 = 125
  8.) 1.5 ^ 3 = 3.375
  9.) 9 = -3 ^ 2
10.) 16 = -4 ^ 2
11.) 25 = -5 ^ 2
12.) 6.25 = -2.5 ^ 2
13.) -8 = -2 ^ 3
14.) 0 = 0 ^ 2
15.) 1 = 1 ^ 3
16.) 1 = 3 ^ 0
17.) 9 ^ 0.5 = 3
18.) 49 ^ 0.5 = 7
19.) 64 ^ 0.5 = 8
20.) 6.25 ^ 0.5 = 2.5
21.) 27 ^ 0.333 = 3
22.) 16 ^ 0.25 = 2
23.) 16 ^ 0.75 = 8
24.) 5.0625 ^ 0.25 = 1.5
25.) 6 = 216 ^ 0.333
26.) 0 = 0 ^ 0.5
27.) 1 = 1 ^ 0.25
28.) 7.5 = 7.5 ^ 1
29.) 0.125 = 8 ^ -1
30.) 0.0625 = 4 ^ -2
31.) 0.25 = 16 ^ -0.5
32.) 1.413 = 2 ^ 0.5

Dictionary So Far

Symbol

Frequency Shift

Meaning

A 84.7 Hz Statement terminator
B 100.7 Hz Unary digit (BB is 2, BBB is 3, etc.)
C 119.8 Hz Binary digit 0 (most significant digit on the right)
D 142.4 Hz Binary digit 1 (most significant digit on the right)
E 169.4 Hz Equals sign
F 201.5 Hz Number separator
G 239.6 Hz Addition
H 284.9 Hz Subtraction
I 338.8 Hz Unary minus sign (negative numbers)
J 402.9 Hz Multiplication
K 479.1 Hz Division
L 569.8 Hz Binary point (separates integer part and fraction)
M 677.6 Hz Raising to a power

 

Concepts Learned on Page #7

Symbol M represents raising to a power
Integers raised to integer powers
Real numbers raised to integer powers
Real numbers raised to fractional powers (e.g., square root, cube root)
Zero raised to any power equals zero
One raised to any power equals one
Any nonzero number raised to the power of zero equals one
Any nonzero number raised to the power of one equals itself