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This Concept Map, created with IHMC CmapTools, has information related to: Genes and memes.cmap, GENES AND MEMES 2. Combinatorial Hierarchy (CH) was the first attempt to answer the question and was inspired by num- ber theory. a) Hilbert conjectured that that there might be an infi- te hierarchy of Mersenne primes M_n=2^n-1, n so- me prime (not any prime), constructible by an iterati- ve process. b) The formula would be M(n)= 2^(M(n-1))-1 M(1)=2. The first Mersenne primes would be 3,7,127, 2^127-1. After this the computational po- wer of recent computers is not enough check whether next candidate is prime. c) These Mersennes might relate to a hierarchy of Boolean algebras (B). The lowest B would contain 3 statements and obtained from Boolean algebra with 4 statements (2 bits) by throwing out one to get 3 statements., GENES AND MEMES 2. d) The thrown out statement could correspond to empty set in the set theoretic reali- zation of Boolean algebra. Analogous interpretation can be found in other reali- zations such as realization in terms of fermionic Fock sta- tes. e) Half of the statements of Boolean algebra can be true simultataneously as analogs of axioms of a mathematical system. Now the number would be 2. For n-bit Boolean algebra it is 2^(n-1). f) One can form statements about all statements of n- element Boolean algebra: this gives 2^n statements: this corresponds kind of ref- lective level of Boolean con- sciousness. This gives 2^n-1 realizable statements and 2^(n-1) statements, which can be true simultaneously. g) Question: Could CH rep- resent an infinite hierarchy of reflective levels of Boolean consciousness with number of statements with Mersenne prime giving the number of realizable statements?, GENES AND MEMES 3. How could this relate to genetic and memetic codes? a) The next code - call it memetic code - would contain 2^126 codons realizable as sequences of 21 DNA codons. b) For M(4)=127 reali- zable statements and 2^6=64 statements, which can be true simultaneous- ly. Could DNA codons re- presentthese 64 state- ments? c) One can also try to understand the emergen- ce of number 21 of ami- no-acids with stopping sign counted as "amino- acid". Number M(4)-1=126=6×21 is divisible by 21 and by the number 6 of inde- pendent bits of gene- tic codon. Is this a mere co-incidence or something deeper? d) This observation holds true also a the next level. The number of of bits is 126 and divides the number 2^127-2. Num- ber N=2^126-1)/63 would give the number of memetic "amino- acids"., GENES AND MEMES 1. Genetic code: a) DNA and RNA codons represent 6 bits giving 2^6=64 different codons. There are 20 aminoacids. b) DNA codons are map- ped to 20 aminoacids and and there are 3 stop- ping codons stopping the translation. Stopping could be formally regar- ded as aminoacid. c) Given aminoacid A is coded bby certain number n(A) of DNA codons. d) Question: Are these numbers completely acci- dental as the belief in random mutations as driver of evolution would suggest or are there so- me deeper reasons for why they are just what they are? e) TGD has inspired seve- ral proposals in attempts to answer the question. The first class of trials are mathematics based and second class physics based.
