Explaining life in terms of the statistical theory of entropy

"How would we express in terms of the statistical theory the marvellous faculty of a living organism, by which it delays the decay into thermodynamical equilibrium (death)? We said before: 'It feeds upon negative entropy', attracting, as it were, a stream of negative entropy upon itself, to compensate the entropy increase it produces by living and thus to maintain itself on a stationary and fairly low entropy level.

"If D is a measure of disorder, its reciprocal 1/D, can be regarded as a direct measure of order. Since the logarithm of 1/D is just minus the logarithm of D, we can write Boltzmann's equation thus:

- (entropy) = k log (1/D)

Hence the awkward expression 'negative entropy' can be replaced by a better one: entropy, taken with the negative sign, is itself a measure of order. Thus the device by which an organism maintains itself stationary at a fairly high level of orderliness ( = fairly low level of entropy) really consists in continually sucking orderliness from its environment. This conclusion is less paradoxical than it appears at first sight. Rather could it be blamed for triviality. Indeed, in the case of higher animals we know the kind of orderliness they feed upon well enough, viz. the extremely well-ordered state of matter in more or less complicated organic compounds, which serve them as food stuffs. After utilizing it they return it in a very much degraded form — not entirely degraded, however, for plants can still make use of it. (These, of course, have their most powerful supply of 'negative entropy' in the sunlight.)" (pp. 73-73)

from Erwin Schrodinger's "What is life?"

Entropy defined

"What is entropy? Let me first emphasize that it is not a hazy concept or idea, by a measurable physical quantity just like the length of a rod, the temperature at any given point of a body, the heat of fusion of a given crystal or the specific heat of any given substance. At the absolute zero point of temperature (roughly - 273°C) the entropy of any substance is zero. When you bring the substance into any other state by slow, reversible little steps (even if thereby the substance changes its physical or chemical nature or splits into two or more parts of different physical or chemical nature) the entropy increases by an amount which is computed by dividing every little portion of heat you had to supply in the procedure by the absolute temperature at which it was applied — and by summing up all the small contributions" (p. 71). 

"Much more important for us here is the bearing on the statistical concept of order and disorder, a connection that was revealed by the investigations of Boltzmann and Gibbs in statistical physics. This too is an exact quantitative connection, and is expressed by 

entropy = k log D,

where k is the so-called Boltzmann constant ( =  3.2983×10⁻²⁴ cal./°C) and D a quantitative measure of the atomistic disorder of the body in question. To give an exact explanation of this quantity D in brief non-technical terms is well-nigh impossible. The disorder it indicates is partly that of heat motion, party that which consists in different kinds of atoms or molecules being mixed at random, instead of being neatly separated ..." (p. 72). 

as quoted in Erwin Schrodinger's "What is life?"

Life's characteristic feature: staving off max entropy

"What is the characteristic feature of life? When is a piece of matter said to be alive? When it goes on 'doing something', moving, exchanging material with its environment, and so forth, and that for a much longer period than we would expect an inanimate piece of matter to 'keep going' under similar circumstances. When a system that is not alive is isolated or placed in a uniform environment, all motion usually comes to a standstill very soon as a result of various kinds of friction; differences of electric or chemical potential are equalized, substances which tend to form a chemical compound do so,  temperature becomes uniform by heat conduction. After that the whole system fades away into a dead, inert lump of matter. A permanent state is reached, in which no observable events occur. The physicist calls this the state of thermodynamical equilibrium, or of 'maximum entropy'" (p. 69).

from Erwin Schrodinger's "What Is Life?"

This conceptualization of life as an organization of matter into a set of persisting interactions with its environment that lend some kind of creedence to the possibility of seeing the originating conditions of life as a sort of gravitational effect to the substances that adhere for a duration to the scaffolding of an organism as it is in the process of self-organizing. But is there a crucial component in the whole ensemble or is there just some 'emergent effect' of the whole together? This is hard to figure out. I used to look at intelligence as a feature of the selective membrane, the basic datum of in/out as a configuration of space and time, and perhaps that is the essential character of the thing. Or is there something underneath this? Some life/intelligence Brownian motion that stirs a thing into an organism with orchestrated actions?

There's a concept concerning tensors that attempts to describe the actions of things like electromagnetism, that is, it's thingness in the fact that two objects can attract or repel each other at some critical distance, which gives the intervening medium some character that needs to be described. How this 'force' operates at a distance is the thing in the question: 'how is electromagnetism a thing?'

Some of the hokier, new-agey visions of the earth as this resonant structure that gives all the things around it a similar harmonic is both dream-catchery and in and of itself true. Perhaps, this 'crystalline' feature of DNA is a feature of the earth's iron core emanating a harmonic field that establishes an affordable 'low energy state' to the possible configuration of proteins in the lattice work of DNA that we know. That, at the foundation of the DNA is a recording medium enabled by the harmonics of a rotating ferrous 'plasma' core that is perturbed continuously by the day-to-day features of existing bathed in the electromagnetic radiation of a sun to produce the all the little 'evolving' chemistry experiments in the vast biomass of single-celled life in this world. Everything above that level is simply an afforded compilation of possible collaborations between various discreet versions of these single-celled life forms and the various lab bench chemical transformations they allow within the confines of their selective membranes. 

x-ray induced mutation in genetic material: the minimum volume required

In discussing x-ray induced mutations in drosophila flies, Schrodinger denotes the method and target as such: No matter the type of radiation source (speaking in terms of x-ray to gamma rays here) as the dosage goes up, so does the mutation rate. The target for measuring this ionization here, aside from those irradiated drosophila flies, is called the 'standard substance,' that being air. It's chosen "not only for convenience, but also for the reason that organic tissues are composed of elements of the same atomic weight as air. A lower limit for the amount of ionizations or allied processes (excitations) in the tissue obtained simply by multiplying the number of ionizations in air by the ratio of the densities. It is thus fairly obvious, and is confirmed by a more critical investigation, that the single-event, causing a mutation, is just an ionization (or similar process) occurring within some 'critical' volume of the germ cell" (p. 44). 

So, given a dosage of radiation, this 'critical volume' demonstrates the effects of irradiation through ionization. Ionization is when an atom is hit by a 'packet of energy' enough to excite the electron in its outermost shell, causing it to break off (ionization). In large enough examples, ionization, is at the heart of the photoelectric effect. That is, if you heat something (i.e., add energy to it) you cause that something to give off light. Imagine a person's hand giving off light after being hit by a gamma ray burst from a criticality event. Bad news, dude, bad news. 

Now what is this 'critical volume of the germ cell?' That's the specific size (in volume) of genetic material that gets hit by a dose of radiation. Citing the seminal paper on this study of x-ray induced mutation, Schrodinger writes. "He arrives there at a size of only about ten average atomic distances cubed, containing thus only about 10^3 = a thousand atoms. The simplest interpretation of this result is that there is a fair chance of producing that mutation when an ionization (or excitation) occurs not more than about '10 atoms away' from some particular spot in the chromosome" (p. 44).

Armed with this knowledge Schrodinger notes that threats to humanity through ionizing radiation aren't of great concern if known sources of this radiation are regulated. He produces a simple example and leaves with a cautionary note. "To put it drastically, though perhaps a little naively, the injuriousness of a marriage between first cousins might very well be increased by the fact that their grandmother had served for a very long period as an X-ray nurse. It is not a point that need worry any individual personally. But any possibility of gradually infecting the human race with unwanted latent mutations ought to be a matter of concern to the community" (p. 45). 

As an aside, I had read a book in my youth called 'The Therapy of Desire' by Martha Nussbaum wherein she outlines the developmental projects of various schools of Greek philosophy, resting upon their approach to both the passions and their obverse, stagnation. The point of her book, and the preliminary work of these Greek schools of thought, was to teach individuals how to regulate themselves optimally as a matter of a personal ethic. Her source material on the Epicureans and the Stoics reveal whole tranches of what would become Christian teaching that it struck me very hard how much of Christianity as it passed through Greek hands carried that very flavor of the learned community working with the basic story of the Χρίστος (Christos). Likewise, here I feel as if Schrodinger is setting the groundwork for a generation of X-men comics and their backstories, namely the fear of irradiation and the prospects that 'just the right dose' could produce a 'superman.' And as we all know, Kal-El, the original Superman derived his source of power from the sun's radiation. 

Permanence, according to Erwin Schrodinger

Under the heading 'Permanence' Schrodinger writes the following concluding remarks for his chapter introducing the book's topic: chromosomes as the material basis of heredity. 

"Let us now turn to the second highly relevant question: What degree of permanence do we encounter in hereditary properties and what must we therefore attribute to the material structures which carry them?

"The answer to this can really be given without any special investigation. The mere fact that we speak of hereditary properties indicates that we recognize the permanence to be almost absolute. For we must not forget that what is passed on by the parent to the child is not just this or that peculiarity, a hooked nose, short fingers, a tendency to rheumatism, haemophilia, dichromasy, etc. Such features we may conveniently select for studying the laws of heredity. But actually it is the whole (four-dimensional) pattern of the 'phenotype', the visible and manifest nature of the individual, which is reproduced without appreciable change for generations, permanent within centuries -- though not within tens of thousands of years -- and borne at each transmission by the material structure of the nuclei of the two cells which unite to form the fertilized egg cell. That is a marvel -- than which only one is greater; one that, if intimately connected with it, yet lies on a different plane. I mean the fact that we, whose total being is entirely based on a marvellous interplay of this very kind, yet possess the power of acquiring considerable knowledge about it. I think it is possible that this knowledge may advance to little short of a complete understanding -- of the first marvel. The second may well be beyond human understanding." (p. 31).

First, what is the first question? Schrodinger writes: "The first is the size -- or, better, the maximum size -- of such a carrier; in other words, to how small a volume can we trace the location" (p. 29)? What he's referring to is those locations in the strand of a chromosome during mitosis, that remain discrete and intact during the process of cell division. These, as we know, are called 'genes.' At the time Schrodinger was writing this, he was at the forefront of the study of heredity, not himself, but in knowing the experimental methods their value and their obvious limitations. Then, a gene size, measured by volume was estimated at 300 angstroms, that is, 100 to 150 atomic units on any given side in a liquid or solid. So, a discreet unit of heredity, in general, and in 1944 (when it was written) contained "certainly not more than a million or a few million atoms" (p. 30). 

As noted, Schrodinger, who was at the forefront of physics, was here lecturing at Cambridge and rubbing elbows with the foremost in the study of genetics then. And with his insight from doing experiments in statistical physics he was left pondering 'how?' stemming from his realization about the relative size of a gene, as it seemed to counter a rule in statistical physics, √n.

√n, which in statistical physics, is a 'law' regarding the amount of 'volume of something' required for 'orderly and lawful' behavior. That is, under the hurdy-gurdy of particle movement, a volume of 'something' needs to be large enough for one to say relatively stable things about its behavior, otherwise, that volume behaves in ways about which one cannot really say much accurately. On this point, the then-current 'volume' of a chromosome was on the order of 300 angstroms in volume or approximately 100 to 150 atomic distances in length on any given side. The two insights that spin off from this, according to Schrodinger, is that such a small gene could pass on stable features of visible heritability, and second that the stable organism produced could go on to understand this process in every detail. That point, he notes, may elude us. We know the process of how we are, but we may never know the process of how we know we are based upon the simplicity of it all.

This is an interesting point, nonetheless, and by way of an analogy between artifact and culture or word and idea it may show that the materiality of genetic inheritance carries a similar analogy as that of saying the Bible is Christianity, the Constitution is the United States, or the musical notation is Bach's Brandenburg Concertos. The lore concerning the last analogy reveals that the Bach's concertos, in their written form as musical notation were a gift to the Margrave of Brandenburg and were left unheard for centuries because no standing orchestra in the world had the skill to perform them. And perhaps the short, pithy answer to Schrodinger's question is that genes are nature's napkin math of relativity, it's rough sketch of the Mona Lisa, a low-information stand-in for the positions of things, the map that allows you to navigate the territory without dragging every turtle, rock, cactus, and river along with it.

There's a subtlety to this argument that is easily lost. I'm reminded of a documentary on the computer interface and the bulk of it was formed from a compilation of various interviews with the developers there working on the first computer interfaces. And at some point, in one of the interviews, the interviewee, a developer of an early version of the WSYSIG visual interface for a computer user to navigate, call up, and manipulate a computer's resources made the point that he was part of a group making something vastly different from the desktop with papers on it. But that point of departure was lost in translation from the days of the XeroxPARC researchers and the Macintosh or the Windows OS's that developed from it. We ended up with stable documents that lacked the dynamic call up properties that these researchers were trying to conjure, and partly that happens because they were working with information, words, that had until then, mostly existed in discrete locations like books or on sheets of paper. In addition, they also bound this information in boxes, which also lent itself to discreteness: documents, and books. And before you know it, the stability of authorship and property was smuggled into the definition of digital, computer-based communication. Then, the big point was a dynamic object based upon what was needed on an as needed basis built from all the keyword linkages. What we were left with was a version of authorship as stable as the digital metaphor of objects on a screen along with the regulated functionality-- and in some cases, ease-of-use--of possible ways to manipulate this object, such as copying or saving it elsewhere. 

I have gotten ahead of myself. The point of Schrodinger's realization is that such a small volume of atomic material could represent some material aspect of heredity and that, taken together, all these strands of heredity could constitute a future Bach or Einstein, which is a seemingly much more complex and dynamic organism that the mere chromosome strands from which they were created. 

More must be said about the organization of matter within volumes of space, where organization is the stability of a molecule, which is itself a complex chain of bonds among atoms, which impart upon the final construction a form with polarity and binding sites for other kinds of molecules. But once we've gone here, we've already gone from inventing the wheel to finding ourselves in the middle of LA rush-hour traffic. This seems to give us a hint at how much that first step from simple atoms to their stable combinations has achieved and subsequently 'unlocked' potentially. I'm reminded of an interview with Lee Cronin, who simply states that life is atoms solving search in chemical space, and there's something so basic, so subtle, and yet so astronomically important all thrown in that it bears repeating. Life is how atoms have solved for search in chemical space. And now, we can throw in backpropagation schematics of AIs simply to demonstrate that vector calculus and the constant modulation of the two factors can be one way to simplify decision making as the solving of some x,y, coordinate approximation of a larger problem, which itself could be simply about its x,y coordinate approximation, and in a sense the vast universe of possible arrangements of vectors is all that needs to be focused on to conquer the comparatively probable case where some atoms or some chemicals aren't always available in a state where they can be usable for molecules, whereas maybe there's a word out there if only you knew it but that so long as you have knowledge of speech you have the capability to speak it. 

I want to end this lengthy harangue, of sorts, to say that stable molecules are the means by which the universe speaks. And having achieved this speech, the potential for all the possible permutations of speech have become unlocked. 

The aperiodic crystal argument

 "... the most essential part of a cell--the chromosome fibre--may suitably be called an aperiodic crystal."

(p. 5)

from Erwin Shrodinger's "What is life?"

Dynamism in a universal state

But it is the function of a universal state to provide repose for a society long distracted by a time of troubles. A universal state inspired by dynamic and revolutionary ideas is a contradiction in terms, a lullaby performed on a trombone.

p. 537

In Arnold Toynbee's 'A Study of History: Volume 1'