In his 1944 book What is Life?, the physicist Erwin Schrödinger made the famous prediction that the genetic substance (later identified as DNA) is structured as a kind of "aperiodic crystal." He made this prediction by surveying the increasing consensus that chromosomes were important units of cellular heredity, with genes (and their mutations) as smaller, discrete units localized to chromosomes. He then considered, what sort of matter would qualify as the genetic substance? Those words “aperiodic crystal” anticipated the structure of nucleic acids like DNA -- molecules so large as to be condensable into discrete microscopic units (chromosomes) but capable of storing and transmitting huge quantities of information.
Schrödinger sets up a comparison between a clockwork, as an example of a complicated machine, and an organism. He notes that a clockwork is driven by the stored energy in its weights or springs. As the clock "winds down" it functions until it no longer has enough stored energy to work. This sets up the analogy, because the winding (or energizing) of a clock is the like the role chemical (food) potential energy in organisms. In this way, organisms and clocks both need energy or they stop functioning, and so the question could be asked, are organisms complicated machines?
Notice I didn't say, are organisms like complicated machines? Because I think that question can be answered quite easily, yes. But are organisms merely complicated machines or are there other essential differences? Schrödinger's thought experiment helps us answer, no, organism are not complicated machines. At least no category of machine yet devised.
To see this, Schrödinger emphasizes the role of ambient temperature in the functioning of machines versus organisms. A clock can function at a really wide range of temperatures compared to an organism, especially if it was designed to do so. Imagine a grandfather clock, ticking away at room temperature. It has to get pretty hot outside to make the clock stop. And if it's got the right kind of lubricants, there's a pretty low temperature it can operate at. On the other hand, no organisms function while frozen solid, and most have a fairly narrow temperature in the thawed range in which they can function. For most mammals the range is very narrow; a few degrees or so warmer or cooler body temperature makes most mammals feel sick. Organisms that tolerate broader functional temperature ranges, like plants or fish, do so with specific adaptations that are still quite limited compared to the temperature hardiness of artificial machines.
The requirement that organisms function in narrow temperature ranges implies they function in a different way than macroscopic machines like clockworks. To see this, one has to understand what temperature is from the perspective of molecules. Temperature is a measure of molecular movement; the purely disordered and scrambling kind of movement. So, imagine a beautiful, ordered ice snowflake. As the temperature increases, the random thermal motions of the water molecules begin to rail against the ordering interactions of the ice crystal. Eventually, the thermal movement overcomes the forces that hold the water molecules in their ice configuration, and the snowflake melts.
Schrödinger realized that, although cells were still apparently just gooey bags, there must be something in them that was solid-enough. Something that could endure over multiple lifespans, and be passed through the (equally gooey!) mechanisms of heredity. So that's the crystal part of aperiodic crystal; the crystalline state of matter has fixed relative positions of the atoms. Something in that goo had the same kind of regular ordering as a diamond, Schrödinger inferred, and it could be spatially localized to biological structures called chromosomes, which are obviously non-crystalline.
But the regularity of a crystal also vastly lowers its information content. For example, in pure diamond each carbon atom is connected directly to four other carbon atoms (except the surface carbons). So imagine you had a 100 carbon atom diamond, and imagine you could label their positions 1 through 100. If you wrote out the list of atoms it would look like this:
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
That's "C" written out 100 times. Notice that I can summarize the string of C's with only 13 characters:
"C" 100 times.
Because the pure diamond has a simple internal structure, I can compress its description into a much smaller string. The compression is large: 100-13=87 removed characters, or an 87% smaller description. Sometime after Schrödinger, this relationship between the compressibility of a message and how much information content became elaborated into an important area called algorithmic information theory.
Schrödinger's key insight was that, to contain the hereditary information, the genetic crystal must be aperiodic. So imagine that we can replace any carbon atoms we like with silicon (which makes four bonds like carbon). Now the information content of the crystal could be way larger. Let's say we take the 100 atom crystal, and it looks like this:
SiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiSiCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
That's not that much more complicated than before! We can still compress it drastically:
"Si" 50 times "C" 50 times
That's 25 characters or 75% compression of the information (We are counting the symbol Si as a single character; we could use S as a placeholder but that looks too much like sulfur.) But how about this one, where the position of a C or Si is random:
CSiSiCCCCSiSiSiCSiCSiCCSiCSiCSiSiSiSiCCSiSiCCCCSiSiSiSiCCCSiSiSiSiSiCCSiSiCSiSiCSiCSiSiCCSiSiCCCCSiSiCSiCSiSiCSiCCSiCSiSiSiSiCSiSiCCSiCCSiSiCSiCCCSiSiCC
This one is much more difficult to simplify! It's approaching uncompressibility, or a string that is so unpatterned as to be impossible to replace with a shorter description. It's approaching maximal aperiodicity. One may be able to shorten it with a scheme that invents new vocabulary, like writing "A" for "CC" and "B" for SiSi", but the rules for explaining the new vocabulary have their own information content, so a proper accounting of all the information will show that it's hard to make the above notation succinct in any way.
This is how Schrödinger inferred that a molecule like DNA must exist. Organisms needed something that was solid enough to have a highly ordered structure, but irregular enough to have a large capacity for storing information. Only an molecule with high amounts of ordering, but with capacity for aperiodicity, would be able to withstand the scrambling tendencies of thermal motion.
Finally, I note that in explaining how the cause-and-effect patterns of genetics can be transmitted from within the apparently disordered and thermalized world of cells, Schrödinger is aware of the prevailing philosophical implications of determinism and free will. He closes with constraining some of the implications that could be taken from his line of inquiry. For example, he is very explicit in stating that quantum indeterminancy plays no biologically relevant role in the events of living bodies. I don’t think he’s offering that because he’s interested in skepticism, but based only on foundational considerations of the length and timescales of biological processes.
In the same, closing section, Schrödinger makes some of the connections between quantum mechanics and the nondual perspectives commonly ascribed to ‘Eastern Philosophy.’ If you’re interested in Schrödinger’s thoughts on Vedanta and the nature of consciousness, you can read the original.