@layman,
Let's just cut to the chase.
layman wrote: "Suppose I take a piece of paper and write today's date on it. I then write words which ask for help and explain that I'm stranded on a small island located at x latitude and z longitude. Assume it's true."
Now, why don't you tell me what you mean by "information" with respect to this, other than the message: that is, quite apart from the writing or its intended meaning. (I don't need to distinguish intended meaning from imputed meaning because you said that this message in a bottle need never be found).
Clearly this is writing (to the writer) and has a meaning (to the writer). That only supports my point, that text exists only insofar as someone recognizes it as such. You haven't shown that ink on paper is INTRINSICALLY text or a message or something mysterious that you claim to distinguish from both.
As for explaining to you why the geneticist made a category error in claiming that genes contain information, until you explain what you mean by information in this context, such an attempt is contraindicated.
I will note, simply to clarify my own position, that DNA does not contain "instructions" any more than dynamite contains instructions for the rocks it explodes. DNA is a molecule which is processed by other molecules according to the laws of chemistry (which are a subset of electromagnetic phenomena).
Use of the term information in this context is part of a modern tendency to confuse nonsentient processes with communication, whether in the realm of biochemistry or electronics. It results from the failure to understand the nature of conceptual isomorphism and of the central role of observers in defining such isomorphisms. This failure is a category error because it conflates different logical categories.