what Crick means, I believe, is that since multiple codons can code for a single amino acid the information or entropy in that set of codons is larger than the information transferred to the protein creating a many-to-one interaction. This means that you could, in principle, create an RNA sequence 'A' that codes for the same protein as another sequence 'B', but they are discretely different implying that this difference could be exploited to send different information back from proteins to this different RNA sequence. Kinda a reach in my opinion and not really important as proving you could do that doesn't bring us any closer to understanding what nature actually does. I guess the most interesting result with this research is analyzing the thermodynamics of this reverse interaction as an argument as to why nature has not evolved a way to do this.
Codons for the same amino acid can have very different efficiencies due to use of different tRNAs. And tRNA abundance varies across organelles (mitochondria), cells, and organs. It is not just protein sequence but also protein abundance and translational progressivity/speed/efficiency and completeness. Reverse translation would not recover these aspects.
I think it was a bad argument, perhaps due to weakness in Crick's knowledge of information science.
The argument goes like this;
Suppose you built a library of chemical reactions, to generate a DNA codon from
an amino acid, and did this for all of the different amino acids.
Since two different DNA sequences comple to the same protein, you could take sequence A, perform transcription and generate a protein P, and then construct a different DNA sequence B.
Thus we have "genetic information" extracted from a protein and stored in DNA, violating the Dogma... in an extremely cheesy way, since it's obviously the same "information" you had at the start, just encoded differently, and also it's not different in any meaningful sense from doing the same reverse engineering on non-logically-redundant DNA.
I think the idea is that this different codon sequence "may" be able to be used by the biological organism in a as yet to be discovered way. So, it wouldn't be useful in producing more proteins but may be able to affect the cell in some other way. I've never heard of anything like that though and the redundant codons is probably just the most thermodynamically efficient route to protein production. Interesting thought though
Redundant codons allows for more fidelity in signal. If you notice for most codons in the codon table the third base in the codon can mutate and still encode for the same amino acid. Now that position in the DNA is more tolerant of receiving a mutation to the point we call it a silent mutation if one is there.
Same protein P is coded by two different sequences, A and B. The "redundancy" observation is just saying that when you find some P molecules in the organism, you can't tell which were coded by A and which by B - that information is, literally, lost in translation. Yes, it's not really lost - it's smeared over the "global state", as DNA sequences are physical objects and A and B have slightly different resource costs, but that's still far from being able to modify DNA based on information from proteins.
FWIW, "redundancy" does have some different interesting functions in nature. Sequences like "AAAA" "ABAB" and "BBBB" are (in this example) equivalent under normal read, but if you shift the reading window one nucleotide to the left or right, those two sequences could code for something else entirely. AFAIK some bacteria exploit that. But again, this is still not a protein->DNA information transfer.
The article doesn’t seem to present any explanation of how his argument supposedly relied on that.