Well, information entropy is isomorphic to thermodynamic entropy. To waste information capacity is to emit energy as waste-heat which could have done useful work.
Of course Nature "tries" to pack in as much meaningful signal as possible!
"DNA stores information at a density per unit volume exceeding any other known medium, from hard disks to quantum holography. It’s so dense that all the world’s digital data could be stored in a dot of DNA the weight of eight paper clips"
Yep, the smallest atom, hydrogen, weights ~ 6 * 10^-23 of a gram [1] (that's 0.000... some 23 zeroes ... and corresponds to 1 "atomic unit"), and other atoms weight just tens or hundreds times more (so still in same ballpark).
The bases (the letters in the four letter DNA alphabet), mostly built up of light atoms, weigh each just a bit over 100 of such tiny parts of a gram (atomic units, or g/mol, to be exact) [2] [3] [4] [5].
They appear in pairs, but still, even given that a pair weighs around 300 * 6 * 10^-23 g, you can fit quite a few of such base pairs in a few grams. Ca 3.3×10^20 / g, or ~ 330 000 000 000 000 000 000, given this rough esti-calculation.
Well ... it seems you might be right. Another estimation states:
"Capable of storing 215 petabytes (215 million gigabytes) in a single gram of DNA, the system could, in principle, store every bit of datum ever recorded by humans in a container about the size and weight of a couple of pickup trucks."
Perhaps they include the weight of stuff like histones [1], which DNA is wound up upon in order not to get entangled. That could add some considerable weight. Also there are various epigenetic modifications on top of that, further adding weight, in DNA in its biological form.
Do you disagree? Back of the envelope-wise (depending on their definition of "digital data"), that seems to be about within two or three zeroes of correct, no?
Well, the 2.9 billion base pairs of the haploid human genome correspond to a maximum of about 725 megabytes of data, since every base pair can be coded by 2 bits.
For a recent book / set of papers on the topic of understanding biological information, I can recommend having a look at the BINP book: http://www.binp.org (Biological Information, New Perspectives).
It is a collection of papers from a symposium on the topic at Cornell University.
I maintain that it takes utter foolishness to not acknowledge the screaming intelligent design behind nature. Seldom does it get clearer than when we as information systems designers study the information systems in nature, and find basically all our "inventions" all there already, in an uber-elegant, uber-effective, uber-smart version.
Heck, even the TCP/IP protocol has its counterpart with the addresstags (post translational modifications), for sorting in the biological router called "golgi apparatus" [1].
We never observed a process creating these structures that doesn't start from already existing such structures, and it's not like we see these structures popping up spontaneously everywhere in the universe. No, we didn't find them elsewhere than on this very planet, out of the hundreds we can observe.
The combination of such ingenuity on every level -- physical and abstract -- with such an astonishing beauty and such purposefullness, also on every level, makes me cringe when the cred for all of this is given to this unobserved idea of evolution .
No, I'm not talking about the changes we do observe in nature today which also go under this term, but on the origin of these solutions and structures.
Or maybe you've got the causality backwards: We humans are the results of a designer-less stochastic evolution, and we internalize its operating principles, which come back out again when we look for "intelligence".
In other words, it's the anthropic principle again: If the universe operated differently, and different patterns were evolved and led to us, then we would consider different patterns to look intelligent.
... and then trust that this designer- and intention-less stochastic, random, evolution brought us brains that tell us the ultimate truth?
Given the heavy biases of the anthropic principle, odds don't look good (... when we can't take back on some intentionality towards anything, behind anything).
Who is talking about ultimate truths? Science is about doing observations and trying to figure out what models explain the observations best, not finding some mystical ultimate truth.
Of course Nature "tries" to pack in as much meaningful signal as possible!