Neil Caithness
March 8, 2018, 4:14 a.m. PST

Hi PerryFrom the Challenge guidelines:

7. The message passed between the encoder and decoder components must be in a sequence of symbols forming characters of a finite alphabet. For this purpose, a “symbol” is a group of k bits considered as a unit. (A more complete definition of “symbol” in the context of this Challenge is set forth on page 340, numbered paragraph 8, of the book, Evolution 2.0). A “character” is a group of n symbols considered as a unit. (For a more complete definition of “character” in the context of this Challenge, see numbered paragraph 9 on page 340 of the book, Evolution 2.0). In the system, n+k must be equal to 5 or more, such that it is a 2-layer system which can represent at least 32 digital states.

"At least 32 digital states" seems to be an error. For a 1-bit system (i.e. k=1, that's two symbols) and a word (or "character") length of four (i.e. n=4, so n+k=5) that's 2^4=16 states. (Note that for the DNA code, k=2 bits required for four symbols (A, C, G, T), and n=3 for triplet codons, n+k=5, that's 4^3=64 states.) So for n+k>=5 the minimum number if states encoded would be 16, not 32 (perhaps a typo slipped in as 2^5=32).

Sorry if I've made a mistake. If there is something on page 340 of your book that points out what my mistake is, please could you post the relevant page?

Also, if I may ask, as an information theorist when you say a 2-layer system, does this refer to symbols grouped as characters as the two layers, or do you mean encoder and decoder as the two layers?

Best regards

Neil Caithness

neil.caithness@gmail.com

@Neil Caithness

n=1 is trivial because an alphabet with only one symbol is not an alphabet.

You’re right, the layers refer to symbols and characters within the message.

n=1 is trivial because an alphabet with only one symbol is not an alphabet.

You’re right, the layers refer to symbols and characters within the message.

Neil Caithness
March 12, 2018, 3:34 p.m. PDT

@Perry MarshallExcept 1 bit is TWO states, 2^4 = 16, not 32.

You're absolutely right. I made the following change to the prize specification in item #7:

OLD

In the system, n+k must be equal to 5 or more, such that it is a 2-layer system which can represent at least 32 digital states.

NEW

In the system, n+k must be equal to 5 or more, such that it is a 2-layer system which can represent at least 16 digital states.

Thank you for pointing out our mistake.

Perry

OLD

In the system, n+k must be equal to 5 or more, such that it is a 2-layer system which can represent at least 32 digital states.

NEW

In the system, n+k must be equal to 5 or more, such that it is a 2-layer system which can represent at least 16 digital states.

Thank you for pointing out our mistake.

Perry