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It looks to me like the mathematics and evolution of DNA can be neither random nor accidental

Betty ... The word "change" applies to everything in the universe, at every moment in time. And that which is happening in each next moment is a randomly predictable change from that in the prior moment -- with high confidence results given good understanding of the process.

OldNavyVet, just take a look at this article, "Darwin: Brilliantly Half-Right; Tragically Half-Wrong", by Perry S. Marshall.

Of course I agree with you that change applies to everything in the phenomenal or material universe. Things are constantly changing all the time. But what on earth is a "randomly predictable change?" Your argument appears to be strictly, relentlessly deterministic.

Whatever. What Marshall wants to know is —

Is the formula
Random Mutation + Natural Selection + Time = Design
Mathematically true, or false? ...

This is Darwin's formula for biological evolution. But does it hold water?

DNA is a blueprint for life. It’s a code and a language. It has an alphabet (A = Adenine, G = Guanine, T = Thymine, C = Cytosine) and that alphabet spells out the instructions for everything. So the question is:
Can Random Mutation add information to DNA?

To analyze this question, Marshall invokes Claude Shannon's information theory. And he finds that "random mutation" is "noise" with respect to DNA. Noise in a communication system degrades the message being communicated. That is, it doesn't add new, useful information, it just degrades the information being communicated. In short, mutations are deleterious, not the source of a "new and improved" biological individual/species.

[Alamo-Girl, you are going to love this article!]

Marshall asks, "has any advocate of Darwinian evolution ever proven that random mutation can increase information?" The answer evidently is: No.

It’s interesting to note that the fanatical atheist Richard Dawkins, perhaps the most famous living proponent of Evolutionary theory, has never answered this question either — in fact he has studiously avoided it. There’s an article [http://trueorigins.org/dawkinfo.asp] where this question was posed to Dawkins, and even though six years have gone by, he never answers it. The answer he does give is a smoke-and-mirrors example at best.

Somehow, I don't find that surprising at all. But what it all boils down to is this:

But there’s one kind of design that does not occur naturally, so far as anyone knows:
What does NOT occur naturally is CODES. [DNA is a CODE.]
Symbolic codes of any kind — things that contain language, a message, or information, any arrangement of symbols that represent something other than itself — do not happen naturally. Blueprints, languages, ciphers, encoding / decoding mechanisms all come from a mind.
Just as there are no exceptions to the law of gravity, or the laws of entropy, there are no exceptions to this.
There is vast difference, in fact an infinite chasm, between a pattern and a code. Patterns occur naturally [e.g., "Snowflakes, Tornados and Hurricanes, Weather, Stalagmites and Stalactites, Rivers, Sand Dunes, And much more"], codes do not. All codes contain patterns, but not all patterns contain codes. Codes can only come from a mind. There are no known exceptions to this.

Just a little food for thought!

Thanks so much for writing, OldNavyVet!

I forgot to mention tbat random mutation happenings should be factored into probabilistic genetic studies — mutations happen frequently.

From Steve Jones (pg 170) we have:”DNA’s inability to copy itself without mistakes - mutation - means that evolution is inevitable. Natural selection does nothing more than capitalize on that fact.”