Decoding Gödel

Logic Level pending

If Gödel sent you this message:

M = 169384947234470127970664189667684676328531852445081523551226070323144595309784611788521028124086171572652977937886548312500000000 M = 169384947234470127970664189667684676328531852445081523551226070323144595309784611788521028124086171572652977937886548312500000000

Would you be able to understand what he wrote to you in the English Alphabet ?

I am Godel Hello world What a great day! You will never get this

Andrea Tino by Andrea Tino , 34, Netherlands

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1 solution

Andrea Tino
Mar 7, 2016

Gödel's numbers are the result of a particular encoding algorithm performed on sequences of alphabet characters in order to get a number. This technique was created by Gödel while proving his Incompleteness Theorem .

So, the Foundamental Theorem of Arithmetics states that whatever natural number can be factorized in the product of prime numbers. So, just factorize M M in order to get:

M = 2 8 ⋅ 3 5 ⋅ 5 1 2 ⋅ 7 1 2 ⋅ 1 1 1 5 ⋅ 1 3 2 3 ⋅ 1 7 1 5 ⋅ 1 9 1 8 ⋅ 2 3 1 2 ⋅ 2 9 4 M = 2^8 \cdot 3^5 \cdot 5^12 \cdot 7^12 \cdot 11^15 \cdot 13^23 \cdot 17^15 \cdot 19^18 \cdot 23^12 \cdot 29^4

And let's use exponents to get the character being used:

8 5 12 12 15 23 15 18 12 4
H E L L O W O R L D

And there you go!

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