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Axiomatic Panbiogeography

offers an application of incidence geometry to historical biogeography by defining collection localities as points, tracks as lines and generalized tracks as planes.
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What is a mathematician organism?

Applied Metabiology: from toy to tool

Why "provable" evolution matters: -
There is huge difference between mathematics and philosophy with respect to biology than with respect to physics.

Simple outline of the difference might be: one can constuct the concepts
other can only use already constructed concepts.

If the particular metaphyiscal phornomy I imagine functions to create
the dyadic underlying reproductive digtiatlity then it might be
possible to use QM computers' subroutines in DNAcomputer interfaces
to control aspects of biotic potential actually.

Metabiology is a concept constructable or potentially constructable t
with 3 different toy "models" but how it is engineered
is a problem that not even physics can solve since the math
and the philosophy must be always separated.  In typical physics engineered
approaches this is not ....the biological way.

Some of the constructions however can be thought in both the pure
and applied metabiological subjects.  this is a new kind of method \
and stoichiology of operation that did not exist for other sciences and
is the true source of rejection of the discipline. Just too new to understand...

It is interesting to speculate  on Wright's 1931 description of the population genetics of organisms with organs that go to size zero in this post modern framework.  Wright saw genes coming from mitotic irregularities.  I have interpreted this in terms of Kantian "compression" of the soma on the genes already in the gene pool.  The shape of a creature attempts to diminish the space that the genes operate in since if they can do that they can reproduce with less energy/baggage/hardware.  This is the organism with a metabiological body and possible zero size for any given organ.

So the self image is one of genes not metabiologically indifferent even if the organ that a mistaken mitosis opened space where compression could not operate  was penetrable by population genetic forces and thus increased fitness.

Different softwares biologically arise orthogonally to large population adaptabilities.  Thus the first creature was not a mathematician but a programmer.  Population genetics can give us some idea of where the genes come from if we can relate progamme syntax differences to different deflunct organs and semantics as to how the DNA itself can expand the places the compression diminishes.

von Neumann’s Self Reproducing Automata and the discovery of DNA Structure

"I thought this was a thought provoking book, but perhaps was not suited to be a book, yet. It builds on the idea of DNA as software and tries to think of Evolution as a random walk in software space. The idea of DNA as software is not new. If one considers DNA to be software and the other biological processes to also be digital, then one is essentially sweeping out all that might not be digital. This view of biological processes might thus be at best an imprecise metaphor. But as Chaitin quotes Picasso ‘art is a lie that helps us see the truth‘ and explains that this is just a model and the point is to see if anything mathematically interesting can be extracted from such a model."

The real challenge is to find rather a biophysical substrate to instantiate and materialize the mathematician organism Chaitin created. Chaitin already extracted something very interesting mathmatically but limited this to horizontal gene transfer. This was  a let down when it is was supposed to offer some route beyond the differential equations of pattern formation. So what is needed is double population dynamics approximately divided by 2 (with slight differences for attraction vs repulsion based gene fixation Lyapunov exponents per trajectory in orbit).

It does appear that one "is essentially sweeping out all that might not be digital" but if one considers the Lebnizian dyadic as digitial writ large then Kant's Opus Postuum shows that such is not the case.  As this "digital" which would ultimately depend on the fundamental forces of attraction and repulsion binary (surface through repulstions, penetrations by attractions  materially combined by a genetic code) it yields layers and husks etc.  despite being positioned through Leibnitzian dyadical locations. (aka binary logic physicalized).

Interestingly I like Chaitin's idea because I always felt that digital computers which derailed the design of many otherwise analog devises,  inhibited the creation of techno-biology interfaces such as are imagined by molecular programmers.  It remains only to figure out how to make some kind of flow computational assembly link to somatic evolutionary programability and if this can be enhanced from  metabiological epistelology,  all the better. Mayr worte his large work (on proximate biological history) to keep this from happening. Chaitin has seen past this. So should we.

There is no metaphor here. This is an issue of substance.  Biologists in their ontological quest to keep religious designs out missundrsrtood Kant, failed to embrace Cantor's organacist view, and never worked out it's internal molecular vs whole organism viewpoints.

On the use of a grossone Computer to develop increasingly realistic biological models of Chaitin –like algorithmic mutations.

The question the grossone computer is an answer for is, “How can one store infinite numbers in the finite memory of our extant computers?”  Sergeyev has been able to simulate his infinite radix computer concept with current computers.  Thus Sergeyev’s work is in the field of practical applications where one is able to see through some interface practical applications of numerals “observing” numbers.

This approach may seem remote from empirical science since it is often difficult to even try to imagine as a thought experiment how infinite numbers can be used to express finite experimental data.  Yet this is precisely what Chaitin tries do to while opening a door for the existence of metabiology.

Here we show how metabiology can affect theoretical population biology such that increasingly more  realistic empirical models can be developed by exploring algorithmic mutations through time complexity of vicariant time panbiogeography in  a constantly  enlargeable space computed and displayed via grossone computations that expands the syntactic notion of intrinsic rate of  population increase from exponentiations to tetrations to any Ackerman function. The NBS betweetn side effects and teamwork operates post-economically here as a cross intra-interspecific competiton function belt tricked.

And are able to accomplish this by using the least action principle where Fisher used a the more deterministic thought process when exploring comparing blending inheritance and particulate inheritance by analogy with elastic and inelastic collisions of molecules in kinetic gas theory.

Panbiogeography provides the halting place as where the increasing r can not go (because it is so constrained by prior track biogeography which narrows as the expansions attempt to increase. This is experimental metabiology starting over on an infinity computer.

We do not throw away all of the body. The insertion place for instructions is the DNA computer interfaced to hardware thi s software archived or was panbiogeographically exhumed.  We keep that which compresses what only genetic penetration might expand.  We can throw out threat point recapitulations (which ???) but rather to surficial increasing the biotic potential generally. Thus this is not a Platonic ideal organon in a Kantian metamathematical sense but is rather merely a means to do theoretical biology like theoretical physics which the Serbolloni conferences(of late 60s early 70s) were mean to  facilitate but which never happened.

The  explosive power potential of Evolution.


In general evolution is not thought to be something that either was heading towards some particular future (chain-of-being was wrong idea) nor was it’s notion of adaptive radiation considered to be hierarchic in a sense that one radiation and a later one might be predetermined (no Homonculus in the sperm).  Metabiology challenges both of these ideas without one biasing how is to have read the past of evolutionary taught thought.  Because whatever empirical metabiology is or will be it seems so different from what evolution thinking has been Artem Kaznatcheev has suggested that Chaitin the original author of the idea does not prove what he set out to do. 

One must distinguish the relation of math and philosophy as per physics that Chaitin founds vs the use of math in on-going theoretical  biology to truly decide if this criticism is valid or not.  The suggestion that the application of metabiology to real biology can not be of substance remains however as something that is not a mere figment of thought.  What is substantial in metabiology relies on a different view of the potential and kinetics of evolution in nature.  Darwin considered the checks to any potentially ‘explosive’  possible change within an economic modeling “framework”/tradition/functionality and much of theoretical biology relies on particular manifestions within this frame.  Metabiology suggests that broader framework for doing mathematical evolutionary theory exists.  As such to understand what empricial metabiology (of artificial software walks) might apply to natural software analogies factually (DNA as software) it is necessary to show how this enlarged modeling space is different from other suggestions to expand the evolutionary theory places (such as  Hierarchical Selection Theory and Social Infrastructure Selection),  This can be done by considering the relations of adaptive population explosions either being related to prior ones or not and whether or not they have a potential that is predictive of future outbreaks.  HIerachic selection does not permit one adaptive radition to necessarily be set hierarchically within  another but does not deny that such could occur while Social infrastrcutre selection would insist that if this occurs it is only due to a common group gradient of “pleasure” that gives rise to it.  Real biometabiology however both permits one to think of a potential future explosion of new living forms based on the past potential released kinetically and does permit one to go beyond adapation as the mechanicsm that links two different radiations.  It enables one to help understand not only why so few of the many forms of life that are possible and have arisen only a few remain and it helps us to see how these few might explode into something new later.  This is not your Grandfather’s evolution but it relies on all of the past thinking in evolution to evolve to its next step.

Computers do exhaustive searches.  Human beings create bigger and bigger modeling environments (i n sync hopefully with new technologies actually manufactured and used by humanity). Nature through observation and experiment limits the models and the current technology.

This comparison is incorrect since the difference between ID and CRE generation wise is meant to represent the difference between evolution in one lineage that can be separated off from its parental node system.  Fitness cuts across this but ID is always about finding the nodal path points if one already knew how evolution already went.  Humanly we don’t always know how to do this, but given an evolution it is possible to find it when not obliterated by deteriotating processes.  ID is constant for all generations in its ideal where Spinoza replaced Leibniz per math.  This philosophy was missed at this website’s analysis

“A naturalistic mechanism for the proposed oracle is still very much a mystery. However, the architecture of execution routines and the structure of genetic regulatory networks (GRNs) is very similar. From a programming perspective, a hierarchical structure could serve as a heuristic stand-in for this oracle. In particular, an approach called subrecursion (e.g the use of subrecursive hierarchies -- [15]) might provide a mechanism for the supervised maximization of fitness. This is the direction the end of the book should have taken -- however, this might also be work in progress.”

Not true – this depends on the application of information theory to prior  to DNA genetic factors where it is always the case that an absence of the homonuculus in the sperm is the way to the prove of evolution continuing obtains.  It may not be that Von Neumann’s insertion of instructions into the full organism (to get the next mutant) or the lack of a need for self-recursion in the living tissue materiality IN REPRODUCTION exists for empirical metabiology.  Subroutines in Chaitin’s sense and  subrecursion differentitate between  telonomics and telomatics (when teleology can be plausibily excluded).  There remains as with theoretical physics a difference between the evidence and plausibility all the time.  I am suggesting vicarinat time in time complexity but Darwin's dispersal cannot find this (nor can current evolutionary ecology without a population r made by many invidual rs that on design could be made mathematically big like the acceleration of the universe is to our contact with parts of it that we cannot so meet.

“So what are the theorems of evolution? Chaitin does not make them explicit in this book, which is a letdown. And a causal reader gets the sense that Metabiology is simply a reformulation of results already confirmed in the areas of population genetics and digital biology. However, it is interesting that Chaitin has come at these results using a parallel methodology. Perhaps this convergence is the best evidence for evolution by natural selection.”


No it is not.  Chaitin stuck to the Platonic ideal.  Making the transition to biology means making the transition to Physics like Kant did. Then and only then will (not only the convergence be spelled in) but Mayr’s concerns aka essentialism, typology, and lacks in population thinking be grammatical.  The species is not the population.  The gene is not the individual but levels of selection need be get separated from levels of organization, clearly!  This has not happened in the pure math of metabiology but is happening when one tries to do experimental metabiology and real biology with metabiological input (rather than by simple analogy).




Does Chaitin prove Darwin?

We are finally at the central question of this post. To answer this, we need to understand what Darwin achieved. The best approach is to look at Mayr’s (1982) five facts and three inferences that define Darwin’s natural selection:

  • Fact 1: Population increases exponentially if all agents got to reproduce.
    Metabiology: A single agent that doesn’t reproduce
  • Fact 2: Population is stable except for occasional fluctuations.
    Metabiology: There is always one agent, thus stable
  • Fact 3: Resources are limited and relatively constant.
    Metabiology: Resources are not defined.
  • Inference 1: There is a fierce competition for survival with only a small fraction of the progeny of each generation making it to the next.
    Metabiology: Every successful mutation makes it to the next generation.
  • Fact 4: No two agents are exactly the same.
    Metabiology: There is only one agent.
  • Fact 5: Much of this variation is heritable.
    Metabiology: Nothing is heritable, a new mutant has nothing to do with the previous agent except having a higher fitness.
  • Inference 2: Survival depends in part on the heredity of the agent.
    Metabiology: A mutant is created/survives only if more fit than the focal agent.
  • Inference 3: Over generations this produces continual gradual change
    Metabiology: Agent constantly improves in fitness

The only thing to add to the above list is the method for generation variation: random mutation. As we saw before, metabiology uses directed mutation. From the above, it mostly seems like Chaitin and Darwin were concerned about different things. Chaitin doesn’t prove Darwin.

it has randomized directed mutations. Fitness as a basic assumption, static environment, and directed mutations make this a teleological model — a biologist’s nightmare.

This is all not true.  He should not have relied on Mayr.

Theoretical biology begins with a software space.

We want to understand if Darwin's idea is able to apprehend evolutionary theory (evolution in nature)
represented in this theorectical modeling environment.  It may be that Gould's idea of a future
name for evolutionary theory will no longer be termed "Darwinian" even if there was a heritage of
research workers that can be traced back or through a Darwinian legacy. Metabiology is the general field of
modeling environment and should not be confused with the theoretical biology that obtains in it.

This makes the relation of math to biology double as compared with math to physics.  There are classifications
of moving forces and side by side descriptive placments of substances underlying different organic materails
with potentially different moving forces.  Metabiology contains both. Theoretical metabiology has a specific relation
(toy model). Theoretical physics does not need this since it is all about the moving forces themselves.  Mayr tries to
craft a philosophy for biology that is different in some sense but misses this more precise formulation that metabiology
provided informationally.


As you describe them in chapter 5 they do seem random. However, your precise definition of the mutation operator in appendix 2 cannot create organisms of lower fitness. If \beta + 2^{-K} \geq \Omega then the mutant doesn’t halt and has no well-defined fitness. The only time a mutant is defined is when it has a higher fitness, thus this is a directed mutation. Of course, you pick one of the directed mutations at random, and hence I think algorithmic mutations are randomized directed mutations.

Maybe I am missing the point completely, though. I tried to provide a more detailed explanation in my new post:

The point there is how does one understand the Oracle down through empirical metabiology via some philosophy of the software places traversed no matter the theoretical biology for a difference of pressure vs contact in the biophysics.  I can see how to use Panbiogeography to provide the equivalent of the oracle which discards what does not halt.  One is not then subject to the idea that the mutation is so directed.  The mutation is here between the species and gene tree for differences in single collection localities.  Those that do not halt simply give the same trees (molecular and phylogenetic) for signifianct differences in collection locality data used.  These are simply increases in populations that maintain the current equilibrium.  I will be using time complexity in an empriical metabiology rather than the beta + 2^-K as in metabiology proper.

A hill climbing random walk is not the same thing as motion in an adaptive landscape
exactly.  The spaces are different - a software space vs. gene frequency fixation sets.
To the get the analogy or comparison one must descend from
philosophy - to
metabiology - to (software space)
empirical metabiology - to (time complexity, cantorian ordertypes, AIT with actual programs)
theoretical biology - to (moving forces vs subtance places coordinations)
evolutionary theory - to (phylogenetic space)
population genetics (gene frequency space)

To try to combine the hill climbing of gene frequency space and software space without
regards to all of the surfaces in between suggests simply that the relation between math
and philosophy was misunderstood.


I disagree that it is “an upper bound” model. In particular, Chaitin’s mutations are directed, this allows a speed up because drift is not possible, but that would only make a quadratic difference usually. Most important, though, is that his fitness landscape is extremely simple. In the mathematical biology literature, his landscape would be known as a Mt, Fuji landscape — every shortest path is an adaptive path. It has been known since the late 80s that in this sort of landscape, evolution is exponentially faster than exhaustive search (In fact — and this is another non-general feature of Chaitin, but one that plays in his favor as you pointed out — if you allow larger sexual populations then it can be doubly-exponentially faster as I discuss briefly here). Unfortunately, it has also been known that this is NOT a reasonable fitness landscape model for evolution. With a more realistic landscape model evolution where not every shortest path is adaptive, evolution can slow down a lot. One of my recent research projects for instance, shows that in some realistic (i.e. used by biologists) fitness landscapes, evolution is just as slow (asymptotically) as exhaustive search.

If you were to build a fully general fitness landscape model (i.e. what you would need for an “upper bound model” as you describe) then you would have to allow any landscape. Of course, such a model is boring, since it is trivial to build an example landscape where evolution — or actually any algorithm (except quantum ones, where Grover search allows a quadratic speed up, but that is still just 2^{n/2}) — will be as slow as exhaustive search. Simply select one genotype (i.e. string x \in \{0,1\}^n) to have fitness 1 and all other 2^n - 1 strings to have fitness 0. Now, starting at a random point in this landscape and trying to find the fitness peak is equivalent to searching an unordered list of exponential size For comparison, the Mt. Fuji landscape Chaitin useses corresponds to a sorted list, so it is not surprising that ‘intelligent design’ (i.e. binary search) or ‘evolution’ (i.e. randomized binary search — where we take a step in the right direction, but the size of the step is random instead of exactly to the half-way point) is faster than exhaustive linear search.

It is easy to see from the get-go that Chaitin’s model will be unsatisfying. A satisfying model will be one where for some “types of landscapes” evolution is faster that blind search and for some it is slower, and we have some empirical test to check which ones correspond to the one we live in. In this way, Valiant’s machine learning approach (discussed briefly here) is much more interesting. It gives some examples where evolution is possible in polytime and others where it is not. Any interesting result in this field would have to have that sort of structure.

Drift is possible but one mus understand how Darwin's dispersal and that of island biogeography is not able to contain the panbiogeogrpahy (space of STF) of future mutated evolutions (orthoselected).  So far metabiology only speaks about this interms of substances as a whole not in part or as systems of moving forces concussed.  To make the comparison to "shortest path" as adaptive requires one to work out how and why biotic potential r has been taken as measure of fitness for life history differences and then deal with the false biophilosophy of a hardened adaptationism.  Williams imprecisely asserted that there is no "biotic adaptation" .  With Darwin prooved in metabiology the entropy in such is possible and it  clear to me that some kind of teleonomic biotic adaptation is possible physiologiucally.  It is hard to suggest just what the suite of substances are that connote the denotation of such.  But that such is more than probable (a versimultude of stoichologies ) seems certain to me.

"The algorithmic mutation actually combine the act of mutating and selecting into one step, it is a n-bit program that takes the current organism A and outputs a new organism B of higher fitness (note, that it needs an oracle call for the Halting-problem to do so). The probability that A is replaced by B is then 2^{-n}. There is no way to decouple the selection step from the mutation step in an algorithmic mutation, although this is not clear without the technical details which I will postpone until a future post. Chaitin’s model does not have random mutations, it has randomized directed mutations. "

Nope, still not true. They can be decoupled as I began to indicate above where it appears that we have used a depauparte notion of selection by refering to artifical selection.  Building up the husks of the repulsions and attractions through inidivdual to population rs makes huge (laerger than currently availble in evolutionary theory) differences of the mutaiton and the selections.  The phyisology of algorthmic mutations is still a bit far off for me describe in detail of  e-m forces to gravity etc but that it exists is definitely physical and extant.

"I hid the subroutine that computes \Omega_N but we will see that it is a superficial feature. \beta and the N that the algorithm returns are completely equivalent. A larger \beta returns a larger N. "

This is also deceptive.  How divergences and convergences utilize blinking fractals will make apparent what ordertypes could other  wise show how non superficial it was. Beta and N (that the algothrim returns) are not completley equivalent.  Ican imagine cases where the differences are determined by different NCE NBS trajecgtories for fully competition equal cooperation scenarios but with gene coopertation at the beta level.  The N may be equvalent to the beta but only is special recapitulatory scenarios. tt seems to me that the halting of repulsions is not always equivalent to th3e halting of attractions per Fisher evolution converged.  In addition when this diverges but is Wright networked (double physical (say mechanical and e-m) continuua) the differences of pure and apparent attractions must be taken into consideration.

Software space theoretical biology of empirical metabiology may diverge
into a science of where new genes emerge out of differences of strong and weak forces
per gravity compared to e-m and gravity.

The right way of thinking biologically in metabiology according to Chaitin is to think of life constantly evolving such that each lineage has to evolve to keep up with other life since there is some limit to how much life can fit on Earth.  This view allows one to think that this “arms race” can be relaxed if the places to increase are not constant but  increase.  This is a fundamental biological thought found in metabiology.  This thought does not depend on the origin of life since that can only affect the rates of increase that are currently being constrained not that there are rates that are always attempting to increase.  Knowing these rates are necessary for accurate experimental metabiology that attempts to do theoretical biology (adding populations and sex etc ).  Some work in theoretical metabiology is however possible without saying how life arose (whether it arose only on Earth or might have arisen at more than one place etc.) .  The wrong way is just infinite, too infinite to figure out even for the Platonist.  It might be thought to be something that Russell never understood about Cantor but that a Pythagorean biologist might mathematically approach in the future.

Better and better lower bounds on Omega which is what metabiology presently creates is not the hierarchical pattern that can be sought so an empirical metabiology might be written to dig this out. Computational complexity using FORTRAN loops can return this kind of structure when individual rs sum to different population r via different numbers of loops of traversal in tetration space (or higher as better diagonals are found).  This gives up on Plato and returns to the discrete math but population biology is currently a r from a continuum.  Instead we need think of Cantor’s contiuous motion in a discontinuous space and use discrete functions in matricies that are themselves discrete representations. These experiments in which computers do exhaustive searches in these spaces will find those HIGHER functions of r(individual) to r(population) (but need to incorporate sex or cooperation as well) that can be THEN represented as ordertypes in Cantor’s e-numbers which though found exhastively can be decoupled via  structural equations into different Wright path analyses that fuse the Galtonian type legacy to the new statistics of non-fully potential (blended) heritabiloity for the most kinetics contained. Cummulative evolution would not be occurring here but only teleomatic realities that humans can purposively interface to otherwise evolved form-making directums.

There exists an infinite amount of complexity.  It is our application to to see this complex as simple and we do this with grossone software.  Axiomatic panbiogeography provides the reason why this is naturally possible in some kind of hardware.  Determining better and better lower bounds to the display of this irreduced complexity occurs as fewer and fewer collection localitieis are needed to design the node^mass^baseline  per track function.  The possibility that all distribution data can be organized aournd the finite few Ocean basins is the final goal for the Croizat method.  This seems as if this can happen back to the Jurassic but in going beyond this it still remains imaginary if a larger metabiology is needed or if one must incresae the number of baselines into inertial lines that go THROUGH  the Earth and into outer space.
The reason this expanded place for exploring models had not arisen before is because no one tried to explore the conditi itnos where say an increase in mutation equaled a decrease in selection WITHIN the network Wright ijmagined connected these possibiliies.  A metabiological increase in mutation has a set of populations, sex, biogeography in which  less selection (ID) could have given  the same result.  To find these living conditions

it is necessary to theorize the extent that population expansions (which divides into ordinal (aggregation position) and cardinal (contributiopn to effective population size) can change the environment independent of any other genome recombination.  The advance contained in this new approach is to realize that gene parts (repulsions and attractions) do this no matter what the genic selection was.  This is how a  least action principle becomes useful.  A given genome has both a potential and kinetic envrionmental affect and effect which on inbreeding expreiments can be display ted. The interchange between selection and mutation thus converts the kinetic back into potential.  If the environment that the genome can tolerate changes however a Fisherian process may arise between networks. That will then depend on the existing deme to life history situation of the species and may require a hieratchhical evoltuionary theory.  A futher exploreation of metabiology should enable one to asses if higher level selections are really any better intutionally than more funding for work in the environment current life can change today.

Metabiology is able to practically extend Levin's (1970)  extended principle ("No stable equilibrium can be attained in an ecological community in which some r components are limited by less than r limiting factors,  In particular, no stable equilibrium is possible if some r species are limited by less than r factors.").  The empirical metabiology being described on this page supports the math where time complexity substitues in what is a large unstable situation.  The tetrational model expands the range of mathmatical relations between paramenters and functions (embedded tetrations of hidden b-d=0s) to which this applies and supplies a much larger number of available r limiting factors than prensently discussed and makes them available for observation, study and denotation.  Tetration is structurally stable in the relation between the individual rs and population r that each species has.  The number of limiting factors as b-d in track^node^mass^baselines are much larger so communities can be thought to be more stable than older theory has so far recognized.  This is the first primary result of empirical metabiology to evolutionary theory itself. The limiting factors are here found INSIDE the organism and that is why they have been missed by all other models of evoulution but this one which shows how biological and mathematical creativity are equipollent but grossone infinite.  Whether math can evolove from here remains to be seen and imagined.

This last statement completes a conversation I had with Simon in the 80s(1983?) to both see "the complex as simple" and to imagine a fractal scaling across all levels of the biological hierarachy dynamically(also presented to Will Provine who did not see it as that interesting).  He insisted that this could only be thought between two levels but hidden developemental b-d=0 individual rs finish what I started in Cornell College Scholar thesis (removed before it was finished by the Cornell administration) as cross level fundament in the evoltuion of worm snake biogeography (difference of discrete and continous morphogeny attempted by the State of Flordia (Sanford of all places) to enter as evidence of nonsense).  I had corresponded with Rene Thom's institution  then but I had  not used tetration (rather Hasudoff dimension.  What seemed simple to me could not be imagined by Simon since he was trying to translate what I was saying into his extended principle but he used a constrained version of structural stability that tetrational systems are not required to follow and yet be structurally stable.  At that time I was sijmply relying on Cantor's assertion of application to biology and not on an algothmically organizated exemplar.  As it turns out Chaitin's reliance on Maynard Smtih's defintion of life (metabolism etc) will also prove too limiting within Levin's community! where mechanism confronts microscopic phenomenolgy during cellular differentiation.  I had simply only then wanted to try to correlate microscopic (alpha and beta kertain pattern differences) snake skin scalation continuites and discontinuties through muscular differences into phylogenies as a practical approach to what I took as "phylogeny recapitulates ontogeny" reversing the usual induction of natural history.  Now I can do this deductively thank to Croziat and Chaitin!!

In contrast to the propositions given by Hastings (Single species dynamics in Theory of Ecology p 112) this is a population level determination
of the births and deaths seen through the social infrastructure selected offsping
in which a deterministic description exists.  Limit cycles can arise from neutrally stable limit
cycles determinsitcally by the belt trick in such a way to simulate randomness wihch
covers the chance nature ofbirths and deaths.

Applied Metabiology:

Although Chatin struggled to imagine sex and got symbiosis instead when attempting to codify the complexity simply,  Feynmann seemd to have also considered the general idea in his lecture on "The Relation of Physics to others Sciences" when discussing bioology.  He remarked that liviing things that work (including plants with no nervous system (no consciousness)) though best thought as a lump of atoms are not simply an atom growing bigger and dividing in half but instead have a complementary hand and glove stratification that splits and reproduces the other other half. Whether he was thinking of the boundary between the hand and the glove as Chatin (sex vs symbiosis) was not said in his use of the notion of information (RNA) but because he knew  Von Neumann well the short and fast may be that this indeed was Feynmann's take on Von Neumann's analogy between DNA and software as he would also think about quantum computers which could exist outside the current reproductive activities of any organism.

The idea that software replaces the machine in the normal science of applied metabiology of course requires a reciprocity between DNA and software and software and DNA.  It seems most likely that software can be thought of as DNA but DNA need not necessarily be thought of as software. It appears that  algorithmic mutations require a cross generational particulate Mendelian compatible  inheritance operating through the hand-glove boundary much like Pearson's view of heritages was different than Galton's (different contribution of different generations to the heritage). The Modern Synthesis thiks in the difference of blending and particulate inheritance only a single generation functionality and yet the evidence supporting the particulate over the continuous (Mendel vs Biometricians) namely of DNA on chromosomes does not  a priori exclude the possiblity of cross generation discrete version reducible to standard Mendelism between among two generations (repulsion and attraction gene parts supply the ontology of this possible epistemological innovation in metabiology).  Thus viruses (Sandin) may not be powerful enough pheonomenologicall to supply the moving force behind the real biological counter part of algorhmic mutation in this cross generational view.  They may be able to multiply a given infinite series but seem to be too weak to enlarge the grossone one inifntity of the series that spans the generations' legacy.

Fitness landscapes as mental and mathematical models of evolution

"Note that in the above passage, Wright implicitly assumes that a population starting away from equilibrium will get to a peak in a reasonable amount of time. However, this is an assumption computer scientists can question by asking what features of a fitness landscape allow evolution to find a peak faster than exhaustive search; this is the question both Chaitin (2009) and Valiant (2009) ask."

Reasonable amount of time however simply means some time different than Lotka's "supplementary time and space information" in which both a slow and fast process is modeled.  If the dual Wright processes that yielded orthogentically are imagined within the deduction of the difference between exhaustive search and cumulative evolution (ie the environment can not change willy nilly as it may under purposive ecosystem enginnering and artificial selections of ID) then Wright and Chaitin are not all that different. The difference simplly respect the power of algorthmic mutations which would follow graphically but what these are are not clear really.  The use of turing machines to compute in grossone suggests a possiblity that will permit such a cross generational mecahnicsm to be reducible to Mendel/Wright and still ask the Chaitin question if there is an analytic function capable of copy at a finite size by processing from infintesimal left or right bias on glove/hand boundary.  The fact that attractions operate to ONE point and repulsions in TWO directions provides a kinematics in which such  space is possible with time so splitting (mobilis).  Historically gene factors were not decomposible to this level because the difference of random changes in base pairs, with random recomination changes , with differences in the chromosome number per copy were not in detail contained theoretically since they were not needed to see the particullate Mendelism from the former blended idea.  I have used catastrophe theory to image such but grossone computation could be possible where DNA copies are associated with grosstwo gross threes (per sets of left and right infinitesimal biases).  In other words the HAND's handedness represents sex while the glove and the hands symbiosis.  The confounding of the two kinds of question (Wright and Chaitin) mentally simply fails to see that these two concepts can be independently decouple with blinking fractals of a expanded particulate inheritance system.  The questions are the same when a metric between the parallels and the orthogonals are defined in  a moving force between evolved parts through the two metaphyscially fundamental forces of attraction and repulsiont.  Thus metabiology builds on the huge expanse since Faraday and Maxwell that Einstein adored where both repulsions and attractions are involved dynamically.  We have to be able to exculde gravity from the possiblity that life may have arisen de novo off Earth while retaining it likely importance within the geographic differences we do currently see ON Earth!

From Physics vs from creative biology

From Physics

The mathematical object observed - Lotka's supplementary space and time info (R expanded)

The instrument - metric in Wright Network for different internalized Fisher integrations contra
Kimura based onrepulsion and attractions in the point/bit change of alleomorph series.

Interrelations between the object and tool.  Does coperation of competition compound the higher rs and

Accuracy of the observersation (how close can the geographic distributions predict the level of looping
in the places where the rs increases and how much does it increase.

The basic mathematical use of grossone is to create a function from an infintesimal (biases left or right
for each bit/point mutation change) in Feynman hand/glove boundary that will copy and yield the magnitude of
the R in the theory (exponential, tetration, ackerman etc).  The geographic places determine how far the current code
can repulse and attract the network and determine where the function can explode into actual infinity.

The project is to determine when and where is this most likley to start - one in what bodies and two where biogegoraphcially.

Finally this will permit intergation to other kinds of life which may operate on other planets and under different codes (chemical bonding relations).
Also it adivsies on how to manage futher exponential growth of the human population.

Theoretical Mathematical Biology – A Grossone Theoretical Metabiology of Populations

Sergeyev  states “the goal of this paper is to study Turing machines using a new approach (grossone infinity computer) and allowing one to write down different finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique frame work.”

Here we show how to combine grossone application  in Turing Machines to a version of  theoretical metabiology which specifies Feynmann’s notion of Chaitin’s software = DNA of Von Neumann as an analytic function biasing from the left or right with respect to the shape of Feynman Hand in Glove to a size capable of being copied.  This copy is defined as the Von Neumann organism that accepts an instruction to replicate itself and calculate a larger number which is bound by the infinite numbers in the grossone framework the analytic functions projects through.  This version of theoretical metabiology is neither pure metabiology (proving results via AIT, Time complexty or Cantorian Ordinals) norpractical  theorectial biology (all DNA as natural software and only understanding how the metabolism and energy are not needed) where selection in nature rules.  This new ontological domain for doing quantitative biology arises because the relation of philosophy and math is different for biology than for physics.  Here specific axiomatic use of the grossone perspective is used to generate the possible linake between AIT results and some aspects of biological reality. This allows one to go beyond  a metabiological Gendanken experiment and is a more realistic version made by use of the math of an infinite radix infinity computer.  Ad hoc genetic hypotheses are provided which makes the qualitiative relation to actual heritdity still suspect but intriguing nonetheless.

We take the Grossone viewed postulates and generate enarlaged versions of postulate 2 and 3 due to the metabiological constraints. In other words we are able to begin to describe the mathematical objects (Weyl  1-D symmetry decompositions to single bit/point mutation changes from a finite whole organism copy recombining genetic factor repulsion and attraction parts population genetics fixed)


The part is less than the whole is bound to the copy size as viewed from Feynman’s idea of complement that grows bigger and divides in half as turing machine von Neumann automata.  We do not say in this version to what extent software as DNA is abetter analogy than DNA as software.  In other words we do not distinguish between sex and symbiosis but we do use populations of copy organisms. Thus the automaton copy of an organism is the finite we operate in and the finite number of organisms in any given population is simply a function of the copy ability (intrinsic rate of increase) but the math that determines how large this number may be finitely may be infinite.

Thus although pure metabiology does not prove Darwin an empricial verification of the biological actions implied may go in some direction to proving that evolution is creative and yet not teleological in (a )nature (except  sometimes where and when man is involved).




History –

Chaitin suggests that Brenner took Von Nuemann’s idea into Molecular Biology. It appears that Feynman had a version of this idea which suggests either that this idea is linked to the Brenner Crick conversation or else the idea of DNA as Software was much larger (or only as large as Feynman’s ideas were bigger than others).  In Physics in Relation to the other sciences Feynmann lectures that biological things do not reproduce like atoms that just get bigger and then divide in half (which is the Von Neumann idea less the instruction) but rather have information in a complement that gets bigger and divides in half.  Since Feynman also thought about quantum computers he need only have thought that this complement was algorthimically divisible in quantum operations (probabilities rather than actual physical properties (as Schrodinger had thought). (This also slightly confounds the idea that Schrodinger’s a periodic crystal was not influential unless Feynmann was really the voice of all science which is not a versimulted of any kind, it would have been remote by any standard.  Feynmann just assumes that an enmuration of all the enzymes and what they interact with and do is suffient for saying what a frog is physically so he did not think about how the mutations might lead to different functions that allow both plants and animals to be working mechanisms.  Metabiology provides some thought in that direction and it is further explored here how gene fixation irreversibility is futher compounded of  weyly 1-D directions in larger space than population genetics uses but fit within AIT.  This is how one has grossone detgerminitc and non determinsitc turning machines where Feynmann did not think but only mentions RNA. 

This is how evolution gets stuck between a Wrightian metric network with Fisherian  channels narrowing the space.  These places are discoverable in panbiogeography and explain where population genetic explosions may be determeined to arise out of in the future.  This is a matemthematical theory of grossone population metabiology.

So whereas the history of the sotware = DNA analogy resides in the genetic code the infinite relation back through a population thinking to the infinitesimal bit point mutation need not result in somatic programs of evo devo as the only outcome. Different topologies of cellular differentiation that are not “programs” can also result in different b-d rs de novo so no deed for all examples to be recapiulatory of genetic revolutions.  The full exploration of this however requires the “hardware” the software changes to be determined and this will depend on the empirical findings from the modeling being true or not.  That is not explored as of yet.

How the new epistemology works:

In this vision for theoretical mathematical biology the fininteness is in both the the total number of individuals in a limited population made of materailly finite lumped genetic factors.  The infinitesimal to infinite trajectory does not however go back the genes but rather to the attractions and repulsion directions infinitely numberd grossone finite corresponded in the record  Thus bias to the left (one non even number in the sequence must relate to the finite organism the species entire finite population numbers for any given length of time prior to explosion to a different relation (all even numbers and half natural ones in this case). Once this is realized in this applied metabiology it becomes  possible to substitute program size complexity with the difference of infinite component of a sequence of 0 and 1 in the particular theory the model laws simply.  One can move from on species to another for a given adapation distributed by moving not from a relation within grossone but by having a grosstwo or grosse3.  Thus the modern synthesis is not a hardening of adaptation but simply due to lack of a matheatmical instrument to say MATHEMATICALLY where new genes come from (panbiogeographically).  The difference between the evolution of dominance by say Fisher and Wright depend much on the biophysics but this new framing does not restrict one to biophysics but only to physics and this is in terms of a kind of quantum like thinking rather than older differential equataion thought.  Orthogeneis is possible on this view as well as some kind of algorithmic mutations within the landscape. One is only able to rearrange the infinite sequence of AIT in grossone computers as far as the genetic code permits repulsions and attractions to compress the higher  population rs given by the copy organisms no matter the irreversibility of genetic fixation.

Here are some thoughts posted on creating in the domain of empricial metabiology ( simulation not proof).


I'm trying to hack a simulation of evolution according to Gregory Chaitin's metabiology model.

Given an algorithm that returns an integer, i need to mutate it randomly trying to get another algorithm that is syntactically right and eventually stops. If the mutation is truly random is impossible to ensure that what you obtain is a valid algorithm that will stop.

My questions are:

  • What is the best turing complete language to do this?
  • Is there any technic from genetic-programming that already attacked this problem?

Thanks in advance

I was thinking in something like:

x <- x + 1

x <- x - 1

y <- x

if x != 0 goto label

this is turing complete and is very easy to modify. What do you think?


edited Aug 1 '11 at 14:24

asked Jul 27 '11 at 19:27




4 Answers


If the mutation is truly random is impossible to ensure that what you obtain is a valid algorithm that will stop.

As Robert B pointed out, a set of Turing-complete functions will satisfy your first part but there is no solution for the problem where you allow the possibility of loops. However, if you remove loops as a possibility then you can generate an expression tree that can provide you with outputs every time you feed it some inputs. The expression tree has finite size and guaranteed termination, or to think of it in another way: to get an expression tree with infinite running time would require that the expression tree has infinite nodes (which would require you to have infinite RAM or disk).

There are strategies for pruning expression trees in order to provide minimal solutions to the problem and some of those strategies involve making the size of the tree part of the fitness function. In other words, when computing fitness, take into account the size of the expression tree: smaller solutions are preferred over larger solutions when everything else is equal (i.e. both solutions have the same accuracy).

answered Dec 12 '11 at 21:26





a nice programming language to use syntax trees is R –  tobiFeb 26 '12 at 23:53


LISP. Well, any homoiconic language. But LISP. Read Koza's books

answered Jul 30 '11 at 19:13



Larry OBrien

What you are looking for here is "Grammatical Evolution", that would be the application of Genetic Programming to evolving working computer programs. This is a good site: Also, you could look into evolution of more basic computing mechanisms like FPGA by typing "FPGA genetic programming" into Google.

answered Aug 11 '11 at 2:16





Well, the first part of your question is about algorithms that are valid. If you define as many functions as you need to ensure Turing-completeness (for example, +, -, *, /, X, Y, Retval, loop, if) then you have satisfied the first part. I recommend using higher-level functions because there are certain structures which will keep evolving again and again, and you'll speed up evolution if you just put it in the list of functions to begin with. For example, loop can be decomposed into if and goto, but with loop you'll save valuable evolution energy, and also ensure validity.

However, your second part is about algorithms that eventually stop. This known to have no solution. One alternative is to set a limit to the number of instructions that a program can execute, and abort the program if it violates that restriction, giving it a high penalty. Or, if you have a terminal which the program needs to load with an answer (e.g. Retval), you can just halt the program and check that terminal.

answered Dec 8 '11 at 15:06

Here is how I will construct a program:

Each organism is a collection locality (species name and lat, long)
Each organism possess a track^node^mass^basline coefficient set that transforms the lat/long into three angles A,B,C which coordinate the phlogenetic tree (species and or gene tree)
A  Mutant organism is the next nearest same species lat/long.
If the mutant coefficient set is able to compute a larger phylogenetic tree  set series without distorting the generalized track and total phylogeny under consideration then themutant coefficients replace that for the programmed "ancestor" (via graph traversal).

After the best distribution of collection localities is made into tracks and best fit of trees are done an exhaustive search (starting from each locality to next mutant) is compared with tracked suggestion and best pick (by changing baseline if necessary) is made.  If the time relations to completion running the program matches linear time, exponential time and quadratic time then the created program is an example of empirical metabiology.

"Key to Chaitin’s notion of evolution is something he calls creativity, and he explored this idea a little bit in a talk at the University of Toronto’s 
Centre for Mathematical Medicine. To understand his first theorems in this area, you need to (roughly) understand the Busy Beaver problem ofTibor Rado. A good precis is here. Essentially, a busy beaver is a Turing machine that operates as long as possible, and then halts. The Busy Beaver function, BB(n), is the highest whole number produced by an n-bit busy beaver."

So instead of the "busy beaver" function I use panbiogeographic phylogenetic tree set constructed size.  The algorthim goes as long as possible to create more trees compatrible with the track the distribution came from.  Adding the looping due to tetration out of the area with individual rs and population rs (thorugh dispersal from what dispersal would add a level of reality to the program but is much more difficult to realize both in principle and practice). Halting is simply the largest graph traversal compatible with track analysis.  Some gremlin walks will not halt but these can be defined out by quaternion algebraic geometry in baselines that meet in the Southern Oceans ( hence Oracle use of panbiogeography). One can begin to think that truely random mutations are being tried if the phylogentic distance between small geographic changef s is large.  Thus when a generalized track contains plants, trees, crafish , fish  and salamanders and single collection differences of each taxon yiled concurrent increases in both the tree sets contained and more congruenence in the used track^node^mass^basline coeficients then the "metabiological mutant" is pretty well random.  In those cases very different genes express the same panbiogeography.  The number of bits, n, in each panbiogeographic metabiological organsim is thus a function of the trees (even polyphleetic) that it coordinates with. Evolution does not necessarily have to start over "from scratch".  That is Darwin's dispersal view.  Here it starts over with a different diagonal argument and othrogeny but it is based on a prior live and Earth evolving together where a common track ontology had preceded (biogeography from prior lineage specific and common biogeography (old idea of endemism in disparate phyla (Croizat's statisitical nature of tracks).

"He really wants to prove an evolutionary process that is, in some sense, cumulative, in addition to being creative"  Croizat had already done this but that is why he was rejected and considerd on the "fringe" since as Chaitin said this is a joke and considerd racist and not politically correct. On the contrary there is every reason to believe so.  Convincing non panbiogeographers may require a further synthetic reality where populations in addition to collection localites are included.  I will work on this.  We will be able to approach the halting probabilty uncertaininty in the next bit by appling grossone computations to the parrelle tracks within the coefficient sets but this going to highly technical and beyon my present (Oct 2013) ability although I see nothing mathematically or philosophically suspect here.

Complexity will thus become associated with increased panbiogeographic track inclusions.  And work will be to see the information in making this complex out as simple (individual tracks that dont affect combined gene and species trees) given Croizat's dispersal from what dispersal (while rejecting Darwin's centerable disperal)(ie using sister vicariances)). The relation back to fitness however does exist this way only it is hard to find a non panbiogeographic reason for it unless it is the hidden (b-d) terms which some will show common tetrations both across phyla dn across individual tracks physiologically ( it would mean something like common forms of double continua in mutiple morphogenies for instance).  I see no evidence either for or against this at the present time.

Introducing such as a generalized environment rather than the one nature supplied (enegetics back to the ecosystem) it will be necessary to relate the histogenies per taxogeny to DNA computers (toehold mediated and entropy driven) to DNA as software through software as DNA.  Yes this might lead to a new trillion $ industry beyond Gates' but that is so far off I can not much think of it often. Entropy and quantum stuff gets in the way.  At this time we might be able to proove that the axiomatic panbiogeographic grossone biotic potential kinetic version is no different formally (biological creatity = mathematical creativity (not as Chaitin had it mc>bc)) than the algorthmic information theortic one but then must decide if Cantor is to be left behind historically.  I am not ready to make that call.

"Chaitin, one of the founders of algorithmic information theory [21], recently suggested [22,23] that:
DNA is essentially a programming language that computes the organism and its functioning;
hence the relevance of the theory of computation for biology.

Brenner said much the same thing in his recent essay in Nature [20]:
The most interesting connection with biology, in my view, is in Turing’s most important
paper: ‘On computable numbers with an application to the Entscheidungsproblem’.
He continues:
Arguably the best examples of Turing’s and von Neumann’s machines are to be found
in biology. Nowhere else are there such complicated systems, in which every organism
contains an internal description of itself.

Indeed, a central element in living systems turns out to be digital: DNA sequences refined by evolution
encode the components and drive the development of all living organisms. All examples of life we
know have the same (genomic) information-based biology. Information, in living beings, is maintained
one-dimensionally through a double-stranded polymer called DNA. Each polymer strand in the DNA
contains exactly the same information, coded in the form of a sequence of four different pairs of bases.
In attempting to deepen our understanding of life, it is therefore natural to turn to computer science."

This is not strictly true. Informaiton is not maintained one-dimensionally.  That statement does not account for the the two-dimensional Turing machines able to produce Turing patterns during morphogensis. I declined to go to Oxford Mathematical Biology Department graduate school because of the unrealisitc application of Turing patterns across phyla (as rxn/diffusion equations) but the argument about the difference of 1 and 2 D does apply there/here.

Information is maintained by the equilibrium between compression and expansion and this in turn depends on the difference betweengeentic penetration and expression.  The DNA only keeps an index of used attractions and repulsions but the community of them expressed in any given organism depends on the internal environment which includes interactions of the 1-D DNA information with the total doubling of the organism cells numbers during embryogeny.  that doubling in the compressive mode can not exactly translate numerically into any particular used attraction and repulsions set but is coordinated to a subset of that information.  Physical chemsitry moves that coordination in wayssuch that no matter the prior penetration larger force (Coming form the environment either internal or external) is always able to narrow what used fundamental forces can express if only given the expansion and not the compression.
"Gregory Chaitin, one of the founders of algorithmic information theory [5] (together with A.
Kolmogorov [15], R. Solomonoff [30] and L. Levin [18], among others), has recently suggested
[6, 7] that:
DNA is essentially a programming language that computes the organism and its
functioning; hence the relevance of the theory of computation for biology.

Indeed, a central element in living systems turns out to be digital: DNA sequences refined by
evolution encode the components and drive the development of all living organisms. All examples
of life we know have the same (genomic) information-based biology. Information, in living beings,
is maintained one-dimensionally through a double-stranded polymer called DNA. Each polymer
strand in the DNA contains exactly the same information, coded in the form of a sequence of four
different pairs of bases. In attempting to deepen our understanding of life, it is therefore natural
to turn to computer science, where the concepts of information, data structures, and algorithms
are investigated."

Again, this is not strictly true.  While life thus thought appears to be digital ( and Kaufmann would love this as it would justify all those Christmasses he spent looking a blinking lights) this is due to the fact that there are only two fundamental force types - attraction and repulsion.  the analogy of DNA to software and software to DNA is not fully/formally reciprocally equivalent.  There would be a difference if irrational numbers could be use or transcendental numbers were used or only real numbers are used in the modeling.  There is a different kind of philosophy being involved here than has traditionally been discussed. Bio-philosophers have also missed elborating this which Virginia approaches largely because E. Mayr has tilted the discussion so much with his proximate and ultimate distinction.  Lewontin long ago knew that simply thinking of DNA as digital was mistaken. Chaitin's work does not remove that thought and his notion of sub-routines getting together is so simplistic it makes Kaufmann's ornaments look like armaments protected no  matter the randomness added to any model.

Both of these examples are not true because Chaitin only really claimed, "DNA is a universal progamming language"  It does not have to have a "central" element.  Darwin was likely mistaken about dispersal and speciation.  Instead it appears that there is vicariant time and a stoichiology of seeming digitiation provided metaphysically only that humans can instruct.  The dimensionality of DNA as a programming language requires what Derrida divided between lexicology and grammetology.  When it is all software as Chaitin sometiems lapses into it is as if the lexicology did not matter but the material grammetolgoical base can  change the infinty of the lexos.  Derrida's attention to Husserl can help to make that point.

Chaitin has an upper bound on cummulative evolution. It is hoped that axiomatic panbiogeography with its tetration out of different areas might give a lower bound. If this bound comes out of the model I outlined abovel then it is likely to be due to constraints from the algebraic quaternion cosets in each muant next mutant computer simulation of the sets of trees compiled.

Program size complexity has its complement in biological metabiology while the size of the program is self-limiting and contained only with tthe same 0,1s that give rise to the program is the relation of the attractions and repulsions in arbitary exanadble cellular space of the protein force field (0,1s are a function of the attraction  to repulsion one way, then the size of the protein with both ways all coded by the triplets.

Grossone as the sack boundary of grain as infinite (avoiding Frege's crticism of Cantor) is isomorphic sensically to the Von Nuemann gene from Turing analogized by Chaitin. in metabiology.  A grossone computer can be used as an instrumenet to more objectively specify what levels of organization biologically preceed ontologifally what levels of selection epistemologically.

Brenner on Schrodinger
"you can see where Schrödinger made his mistake and this can be summarised in one sentence. Schrödinger says the chromosomes contain the information to specify the future organism and the means to execute it and that’s not true."  I noticed this the very first time I ever read Schrodinger after reading that it had the idea of genetics in it.  I could not understand why people thought Schrodinger's idea leads to genetics - IT DID NOT AND NEVER COULD.  It is never the solid crystal structure but the forces that are involved THROUGH its division and resolidification"" that matters (then that is but only in part correct). Von nuemann idea however requires that these force symmetries be strictly seperated between the instruction  ((iunless kant is wrong and liebniz correct (and this is Dyson view unfortunately) and construction (so inserted) but life need not be doing that.  That is why the digital notion needs reduction to the fundamental forces before the clear difference of the hardware and the software that functions metabiologically can be realistically approached in evolutionary biochemistry. Macrothermodyanmic substance stablity applied to toe-hold mediated DNA displacement rxns may allow this difference in force and energy to be instrumentalized but it may also require an infinite computer program to ensure that the compression is separated from the penetration per surface enginneered.  Then I could show the idea of Dyson's digital future  which embraces Von Neumann's gene more or less  is mistaken.

Questões em Metabiologia
Felipe Sobreira AbrahãoDoutorando, HCTE –


Abrahao considers that an organism as it interacts with the enviromnet

is a unverisal turing machine.

It is not that the bits of the program substitute in any way be from the DNA of a living being

Rather the DNA as a programming "lanuage" means that the
forces which undly its dynamics have a possible binary (dyadic (Leibniz)) foundation (but need not be with monads biologicized.

John Maynard Smith's views on biotic potential (Chapman) however are too specific to apply in a future metabiology .  The possiblity of tetration based infinites within  hidden b-d population terms of cells differentiated shows that his view on the relation between bacterial replication and large body individual population replication was not generalizable enough (in Evolutionary Genetics book) to meet the application of metabiology to actual biology,

Again, the "reduction" is not to DNA but to how the DNA bases chemically interact AND are coded into amino acids through two different fundamental forces (attraction and repulsion).

You do not need to abstract the "living" off the body and only have the DNA kintectics within moving.  The dead machine mecahnical aspect of life includes much of what contributes to the "WORKING" of liviing things (Plants are alive even though they have no nerves). Dont think of living and dead but rather of dynamic and kinematic.  There is still room for creativity there.

It is possible to directly ascertain what plays the role of software.  Since each base location can have both repulsive and attractive force relations and if one models selection as the attractive one while containing the amino acid code in the repulsive one a direct analog between metabiology and applied metabiology applies.  One simply needs extend the kinematical into the dyanmic that way.

The recursivity in question (duality of evolutionarily acquired binary(Dyad) forced directions (outside to what and inside how much) thus resides in intracelluar and intercelluar spaces where the forced motions from DNA and both repel and attract other molecular supramolecular structures and molecules.

This is simply not impossible to imagine a priori.  Getting the empirical data for its existence however is.....complicated.

Thus because living things work mechanically in their body we CAN get what Virginia called the metabiological body.  It only seems (because of needing to think past some specific halting) that that horizon of organization (with or without organs but with cells) does not exist.
"Populated by algorithmic organisms, metabiology seems to be deprived of any corporeality. However, the mathematical proof of the existence of a software life-form  primarily driven by creativity, gives rise to a vigorous metaphoric potential that translates directly to the human being in all his dimensions, from our most abstract ideas about ourselves to the most concrete, organic elements of our bodies, because it forces us to reevaluate the neo-darwinist dogma that we are creatures of egotistical competition for survival. Seen from this new metabiological viewpoint, we propose providing the metabiological life-form with a human body or, conversely, providing a metabiological kind of life to the human body, inaugurating in this manner an unexpected
metabiological body.
 Finally, our last topic is to explore possible analogies between the
metabiological body
 and Deleuze and Guattari’s
body without organs
 as conceptual references for a contemporary reworking of the human self-image."

Dion Detterer's Blog


In the last week or so, I’ve been thinking about the relationship between biological complexity and Kolmogorov complexity.

Kolmogorov complexity, put simply, is how much information it takes to describe an object. A string of a million 1s can be described very easily, whereas a truly random string can only be described by itself. A computer programme is a kind of description—what we’re really asking is, “How big is the smallest programme that will describe an object?”

The genome of an organism is essentially the programme used to build that organism, so Kolmogorov complexity seems intuitively to be related. Digging around, I found this lecture by Greg Chaitin, who was involved in the development of algorithmic information theory:"

Well think about it.  A very large vacuum tube computer can compute the same results as my cell phone and yet they use very different amounts of energy.  We need to discriminate between the smallest software programme that gives the same evolutionary trajectory from the smallest amount of energy needed to create a softwart-harware combination capable of producing the same since if it takes less energy and it can be reproduced (inserting instructions) then it will more likely to have evolved and then be observed.  So while the energy and or hardware is not needed in an ideal metabiological archeology practically one must be able to think about what it is in the genome AND its chemical environment that can both describe its own evolutionary trajectory and is the smallest physically ( so it will exist by macrothermodynamic principles) and can be dissected out materially by going to a smaller cut scale and no longer finding any of the objects of the type.

I propose that reason that cells have lipid boundaries is provide space (water/lipid immiscibility) in  which this algorthmic complexity can be recursed by the different effects through attractions and repulsions for the same selected fit genotypic parts in this intra and intercellular spaces under compression of any biotic potential penetration/ expansion of the loci adaptively.

....that provides for a human metabiological corpus phornomically.  Phoronomy directs where the genome instructability for insertion (which was penetrated in times past) is placed (it is divided into a method and stoichiology).  One must attend to the energy and hardware beforfe the method of form based minimization can be non-halted (oracalized).  What is not started over on this view is the genetic code so the only way to build from different origins is with different codes or if life did not exist based on carbon.

Genetic information does not arise principally nor solely by viruses exachanging prior retained loci alterations but rather occurs  while non-gravity repulsive forced mutations provide alternative functionality (same dynamics with different kinematics)  for gravitationally present attraction mediated fixations.

In order to work with real theoretical populations in metabiology using the new post Godel math beyond that continuous stuff used in population genetics it seems to me that an infinity computer can be programmed to work a double dyadic continuum of population genetics with different Lyapunov trajectories per bit and thus achieve the arbitrary digitality required in pure metabiology.

The computer would be specially designed to do population genetic computations from loci selected either through repulsion or attraction which have different infinite representations but start from infintesmially similar starting places.  Thus any given gene may be fixed through an attractive or repulsive  Fisherian  means but result in different Wrigtian infinities for any given divergence across the generations subject to immigration, mutation and selection.

This would be binary programming language in which applied metabiology could be performed.  New genes result when the same distribution occurs as a repulsive and an attractive origins exchange subroutine paths but the total grossnumber system does not need to be increased.  If a different computer is needed to model a given adaptation then a different set of forces may be operative and need to be modeled as part of the genetics itself(are rates of mutation constant etc).

In other words the total is a conditionally  convergent series subsequently rearranged into two divergent series (repulsive-attractive) with grossone algorythmically. Traditional population genetics only had one continuum from which this inference is made in second order logic for the determinism on orbit. Looked at in ceullular automata terms, the conditionally convergent series of remaining the same DNA sequence over time can be accomplished with either a repulsive or an attractive pressure expanding divergently only under a total unified cohesion compressing. That is metabiology on real theoretical populations is

 "a new type of data".

"The introduction of a new way to represent numbers has allowed the author to construct a new device for executing computations on a new type of data. Thus, this innovation opens a completely new page in the whole world of computations. "

"The radix, □, of the infinite positional system is not stored. Its meaning (for example, assumption that □ is the number of elements of the set of even numbers or the number of elements of the set of natural numbers) is a convention for realization and usage of the infinity computer."
The metabiological infinity computer for real population dynamics imagined here DOES "store" the actual infinity (as output graphs GUI interface)(not the infinitesimal divergence) and is thus semantics operated on  given syntax wherein the difference of the even  numbers of elements of the set of natural numbers as different from the set of numbers of the elements of the natural numbers is a convergent attraction-repulsion adapatation representation.  Again it limits as in the original patent as a convention that only a single grosspower is presentable.  Whether a truely metabiological Von Neumann gene automata is constructable is not an issue here and is not this object. This actual infinity is the classic equilibrium in time but modified to include rs based individually. The "convention" can not be patented for some realizations since those are infinite and we (populations existing in a noisy world) are only finite.  Patent lawyers are going to have a hard time working this out.  There is always a versimultude for any and/or all  probabilities that transition between traditional logic units, intermediate logic units, and new arithemetical logical units. The versimultude is never patentable. One will never create a metabiological infintiy computer for modification of actual populations without the device being a part of the population itself. This is because while brains are part of such
 plants have no brains but must have the property in/under current convention and law.  This needs to be declassiifed and made less restrictive. If not done by law it will be accomplished simply through practice.

Bryan Hall

Indiana University Southeast

4201 Grant Line Rd.

Knobview 110

New Albany, IN 47150 USA


"I will argue that Kant’s theory of substance in

the Analogies of Experience faces a dilemma

he cannot overcome with

in the context of



the problem of aff

ection (i.e., is the subject

affected in sensibility

by things-in-themselves, appearances, or somehow



This has to be made on the horizon of developing philosophy where concepts are already intuitable and distributed in works where in the case of natural science had certain mathematics applied. Specifically if there is to be a substance extracted in the work (materialism of some sort) then the forces relevant to its motion are also detectable but formally a result of some combination of attractions and repulsions that are could have been collected in terms of r^2 distances from and within the substance(s) so materialized and real. As this organon is written  down (rather than just being thought) both the appearance and the thing will affect human sense in some way but it must be such that general class of substances applies to force sets that may not effect sense in any animal way.  This may imply that the writing is symbolized in a variable manner for a given lexicology (whether it was a noun or a verb).  This is easy to think when the noun is the substance and the forces are the verbs but given a certain use of symmetry classes in math in the space of the force and substances more complex grammetologies may be invoked and be thus involved if there is necessary progression in the entire reproduction of the animals and plants as a whole.


So if DNA is considered such a Kantian substance, and the genetic code is interpreted as attraction and repulsion force “encoding” of masses of amino acids basically built from electromagnetic force directums and no other forces types (strong, weak, etc) are considered heritably foundational it should be possible to structure the inertial formations that logically possible for all of life as distinct from inorganic bodies before a purpose for such is designed by the remarked dynamics that words symbolically operated as a means to construct the concepts inherent and subsistent.

The transcendental material condition for experience is thus DNA as software materialized from Stars.  Kant had a slightly inaccurate analogy with respect to star physics and this leads to a correction about the ubigquity of the ether vs the caloric as being available to provide the matieral pre-condition to the horizon’s mystic writing pad or versimultde of probability.  Thus it is not the ether and some group of calorics that are apperceived but rather the copyablily of DNA programming phenotypes as particular elemetromagentic force sets with particular substances growing and dividing that conditions the abilty even to write its own being. Once the particular kind of life doing this is given and written then the CPR category classifications can be divided between the substances and forces.  No one has done this because people have not tried to think beyond an RNA world rather than symbolizable attraction repulsion force set per mass as the origin of our (human) known living and biology .  The categories are not applied beyond space and time but rather “beyond” a particular living information reproducibility. Life may exist without so much carbon or be based hypothetically on nuclear forces.  Current life might be tested to be able to use the weak force etc.  There may be a fifth force active  related to gravity etc etc.  These various surfaces of correlation may be truer casues that a future natural history records but we have to do it and just not only think it.  The problem of affection is actually just a simple biophysics of the difference of recessivenenss and dominance across generations but generations of possibly very different only hypothetically real “organic” things (which might be of a different kind of force system as Newton once noted).

Metabiology thus operates here where others had thought that Kant’s metapphyiscs of natural science would have to supply a transcendental condition(Forester).  The object tivity of the categories is related to the difference of applied and pure metabioloogy for signed biological inheritances vs other living  evolutions. Metabiology is thus deconstruction of life itself and as such has a purpose but the biology ofcontributing need not. Metabiology provides spatial schemata for temporal evolutions related to actual biology.  This separated schematism of an outer sense will always be not true and subject to decomposition and deconstruction but by then the concepts were made and the constructions given all the while the organization was changed.