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'

The vulgarization of the dominant minority

Herodotus notes that the Persians, while proclaiming themselves superior to all their neighbors, borrowed their civilian dress from the Medes and a number of outlandish indulgences, including unnatural vice, from the Greeks; and 'the Old Oligarch', in the course of his pungent criticisms of fifth-century Athens, remarks that his fellow-countrymen had been exposed, through their command of the sea, to a more extensive debasement by foreign customs than was to be seen in the cities of less enterprising Greek communities. As for ourselves, our tobacco-smoking commemorates our extermination of the red-skinned aborigines of North America, and coffee-drinking and tea-drinking and polo-playing and pyjama-wearing and Turkish baths commemorate the enthronement of the Frankish man-of-business in the seat of the Ottoman Qaysar-i-Rum and of the Mughal Qaysar-i-Hind, and our jazzing commemorates the enslavement of the African Negro and his transportation across the Atlantic to labour on American soil in plantations which had taken the place of the hunting-grounds of the vanished Red Indians.

p. 521

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

Scientific theology

"The theory of God that emerges from a scientific theology need not posit a magician that flouts the laws of physics. These laws do not describe an unconscious reality; they describe the dynamics of conscious agents, finite and infinite, projected into the language and data structures of the spacetime interface of Homo sapiens. The laws of physics do not describe a machine, in which a marginalized ghost of consciousness must perform paranormal tricks to prove its existence. Consciousness need not flout scientific laws that are themselves projected descriptions of the dynamics of consciousness" (p. 200)

From Donald Hoffman's "The case against reality: Why evolution hid the truth from our eyes

The Interface Theory of Perception

"The interface theory of perception contends that there is a screen--an interface--between us and objective reality. Can we hope to pierce that screen and see objective reality? Conscious realism says yes: we have met reality and it is like us. We are conscious agents, and so is objective reality. Beyond the interface lurks no Kantian noumenon, forever alien and impervious to our inquiry. Instead, we find agents like us: conscious agents. Their variety dwarfs the dazzling diversity of creatures that have paraded the earth and bequeathed to its sediments innumerable petrified mementos of their sojourn. We cannot imagine, concretely, even one new color. We cannot hope to imagine but a fraction of the varied experiences enjoyed by this multifarious host of agents. But despite our diversity, we share a unity: we are all agents, conscious agents." (p. 191)

From Donald Hoffman's "The Case Against Reality: Why Evolution Hid the Truth from Our Eyes

The upshot of Hoffman's ITP in this realization is just how much it 'jives' with Michael Levin's work on xenobots and similar statements concerning consciousness being a fundamental unit of what we see. Likewise, Wolfram's automata and the ruliad guiding their interactions also finds complexity in simple units operating on simple rule sets. And most importantly, his notion is that even these simple structures can be perceived by us as complex because we are merely as complex as them. We can't rule them by constructing a rule that will determine their outcome many discreet moves into the future. We get the same outcome, everything is looking back at us. What we see in the complexity of the world around us is the work of consciousness--ours to see it, and theirs to be seen as such.