The number π is a mathematical constant.

It is the ratio of a circle’s circumference to its diameter, commonly approximated as 3.14159.

π (pi) is an irrational number found in the formulas of many different branches of science, such as trigonometry, geometry, cosmology, number theory, statistics, fractals, thermodynamics, mechanics and electromagnetism. Apparently, pi was found hiding in H-bond energy.

See: Discovery of classic pi formula a ‘cunning piece of magic’


… scientists were still surprised to find it lurking in a quantum mechanics formula for the energy states of the hydrogen atom.

See also: Quantum mechanical derivation of the Wallis formula for π


The Schrödinger equation for the hydrogen atom…

My comment: The Schrödinger equation for the hydrogen atom appears to link π from an infinite series of non-repeating digits to his claims in “What is Life?

UV light has since been linked via the speed of light on contact with water to hydrogen-atom transfer in DNA base pairs.


1) Ultraviolet Absorption Induces Hydrogen-Atom Transfer in G⋅C Watson–Crick DNA Base Pairs in Solution

UV light energy-induced base pair substitutions are linked to 2) A Cellular System for Spatial Signal Decoding in Chemical Gradients.

The cellular gradients are linked to 3) Evolutionary resurrection of flagellar motility via rewiring of the nitrogen regulation system

The links from the cellular gradients in bacteria are linked to the inheritance of mitochondrial (mt)DNA in the organized genomes of vertebrates.

4) Mitogenomic analysis of a 50-generation chicken pedigree reveals a rapid rate of mitochondrial evolution and evidence for paternal mtDNA inheritance

Only four steps are required to link UV light from energy-induced base pair substitutions to nutrient-dependent pheromone-controlled ecological adaptations in chickens.

Viruses steal the energy that sustains the biophysically constrained rate of ecological adaptation to ecological variation. The viruses perturb RNA-mediated protein folding chemistry that is required for paternal inheritance of mtDNA and energy-dependent inheritance of healthy longevity.

See: Epigenetics and Animal Virus Infections

If viruses did not perturb all aspects of protein folding that link atoms to ecosystems, we would seen no variation in the speed at which organisms ecologically adapt. When we see the variations reported in the context of weekend evolution of the bacterial flagellum, they can be compared to ~2 billion years of no morphological changes in bacteria that still live in ocean sediments.

Hundreds of other examples of variation in the speed of ecological adaptation have been reported, and they are typically reported in the context of how quickly individuals of a species might mutate and somehow evolve.

For example: Evolution of stickleback in 50 years on earthquake-uplifted islands

See also: Keeping cool: Enhanced optical reflection and radiative heat dissipation in Saharan silver ants

Interaction among the species that construct ecological niches in the context of ecological variation across several different species were recently exemplified in How curiosity can save species from extinction.


The female lays eggs on wild thyme flower buds. Each caterpillar bores into the bud and eats the growing seeds. It needs all the energy in the seeds to survive, and if more than one caterpillar is sharing the bud they will fight things out in a cannibalistic bout until only one remains. This is a taste of things to come.

After about a week eating the seeds and flower it drops to the ground and waits until it is found by a special species of ant. It excretes a substance that feeds the ant, but also influences the ant’s behaviour. The ant goes and fetches fellow ants that carry the caterpillar down into the nest.

Once inside the nest the caterpillar does a remarkable thing: it feeds on ant larvae until it finally pupates. When it is ready to emerge as a vulnerable new butterfly it begins making sounds that appear to appease the ants. It then emerges, protected by a guard of ants, and climbs up out of the nest to stretch out its wings.

The critical point is that the large blue doesn’t just depend on any old species of ant, but on very particular species. It has evolved to exude chemicals that influence red ants of the species Myrmica sabuleti or M. scabrinodis.

These ants also have very specific requirements, this time in terms of temperature and moisture. If the ground is too hot or too cold they don’t thrive and other species take over.

Ground temperature and moisture depend on the height of the grass. The grass needs to be short, so grazing is important. It turns out that fencing off reserves actually interfered with the life cycle of the butterfly because the grass grew too long, and the ground wasn’t right for the ants.

Similarly, the spread of myxomatosis and reductions in the rabbit populations also meant the grass grew too tall, again altering ground temperature and helping drive the decline in large blue populations.

My comment: The links from a mature egg-laying insect from flower buds to energy-dependent life history transitions  in terms of temperature and moisture linked to the height of grass and rabbit populations defy the claims of evolution touted by neo-Darwinian theorists. All links are equally nutrient energy-dependent and controlled by the physiology of reproduction in every species.  Thus, the extension of concepts from mathematics to physics and biology has become part of mainstream science that is being largely ignored by neo-Darwinian theorists.

For example, see: Mutation-Driven Evolution (p. 199)


In other words, genomic conservation and constraint-breaking mutation is the ultimate source of all biological innovations and the enormous amount of biodiversity in this world. In this view of evolution there is no need of considering teleological elements.

For contrast, see: Self-photosensitization of nonphotosynthetic bacteria for solar-to-chemical production


The absorption of a photon, hν, by CdS produces an electron and hole pair, e and h+. The electron generates a reducing equivalent, [H] (see supplementary text and fig. S1 for elaboration of this process), that is passed on to the Wood-Ljungdahl pathway to synthesize acetic acid from CO2. Cysteine quenches the h+, leading to the oxidized disulfide form, cystine (CySS) (see supplementary text for the full set of reaction equations). The overall photosynthetic reaction is:


My comment: A single amino acid makes a clear difference in the reaction. The difference starts at the level of hydrogen-atom transfer in their photosynthetic reaction. The link to differences in hydrogen-atom transfer in DNA base pairs is also clear. Cysteine is the single amino acid substitution that links what is currently known about the sun’s anti-entropic energy to biophotonics via hydrogen-atom transfer in DNA base pairs.

In my model, energy-dependent base pair substitutions are linked from changes in the nutrient-dependent microRNA/messenger RNA balance to adhesion proteins and RNA-mediated cell type differentation via amino acid substitutions in the histones of supercoiled DNA that protects organized genomes from virus-driven entropy in all living genera. The links from physics to biology are clear. Animal models exemplify the links in the context of all energy-dependent biomass and all biodiversity.

See also: An Illuminated State of Mind


A subsequent study demonstrated that scientists can even implant — we call it ‘incept’ — false memory in the mouse brain,” added Tonegawa. “The challenge is how to extend the information obtained in animal models to human models. The invention of revolutionary noninvasive or low-invasive technologies will be needed, and God knows when that will happen.

For comparison, see: Origins of De Novo Genes in Human and Chimpanzee


Our results indicate that the expression of new loci in the genome takes place at a very high rate and is probably mediated by random mutations that generate new active promoters. These newly expressed transcripts would form the substrate for the evolution of new genes with novel functions.

For contrast, see: The Bull Sperm MicroRNAome and the Effect of Fescue Toxicosis on Sperm MicroRNA Expression

Abstract excerpt:

MicroRNA present in mature sperm appears to not only be left over from spermatogenic processes, but may actually serve important regulatory roles in fertilization and early developmental processes. Further, our results indicate the possibility that environmental changes may impact the expression of specific miRNA.

My comment: Experimental evidence at every level of examination from atoms to ecosystems links the sun’s anti-entropic energy to cell type differentiation via the conserved molecular mechanisms of receptor-mediated RNA methylation and RNA-directed DNA methylation to amino acid substitutions in histones that stabilize the organized genomes of all living genera by protecting them from virus-driven entropy. How can anyone who knows anything about nutrient-dependent cell type differention claim that de novo genes can be linked from random mutations to the evolution of new genes with novel functions. Accumulation mutations link viruses from energy theft to genomic instability and all pathology via the theft of energy in one amino acid substitution.

See: Substitutions Near the Receptor Binding Site Determine Major Antigenic Change During Influenza Virus Evolution

Authors’ comment: The major antigenic changes of the influenza virus are primarily caused by a single amino acid near the receptor binding site.

See also: Why too much evidence can be a bad thing

My comment: It has become perfectly clear that theorists are not willing to believe anything that has been established by experimental evidence of biologically-based cause and effect. Links from physics, to biophysically constrained protein folding and the conserved molecular mechanisms of cell type differentiation in all genera have recently been reported in another species of ant.

See: Bipolar drug turns foraging ants into scouts


We finally have a mechanism to understand ‘nurture’ in molecular terms,” says Gene Robinson, a geneticist at the University of Illinois, Urbana-Champaign, who studies caste determination in honey bees. The ant study, he adds, highlights “how the environment gets under the skin to affect gene expression, and consequently, neural activity and behavior.

My comment: The links from the epigenetic landscape to the physical landscape of DNA via RNA-mediated cell type differentiation linked to neural activity and behavior can be viewed from the perspective of a google search for RNA mediated. The morphological and behavioral phenotypes of all invertebrates and vertebrates have been linked from microbes to humans via a report cited by Robinson in Organizational and activational effects of hormones on insect behavior. I co-authored the cited report, which was published in 1996.

See: From Fertilization to Adult Sexual Behavior

See also: A Deubiquitinating Enzyme Interacts with SIR4 and Regulates Silencing in S. cerevisiae

Both these articles from 1996 have subsequently linked the conserved molecular mechanisms of nutrient-dependent pheromone-controlled RNA-mediated cell type differentiation from yeasts to humans via the conserved molecular mechanisms we detailed in our 1996 review.

See: RNA-mediated epigenetic regulation of gene expression

…co-transcriptional silencing mechanisms form powerful RNA surveillance systems that detect and silence inappropriate transcription events, and provide a memory of these events via self-reinforcing epigenetic loops.

See also:

Here you will find information that links physics, chemistry, and molecular epigenetics via RNA-mediated events such as the de novo creation of olfactory receptor genes in order to encourage a public discussion of a paradigm shift.

Bjorn Brembs and many others have been following the paradigm shift in neuroscience for two decades

See: Watching a paradigm shift in neuroscience

For example see: Role of olfaction in Octopus vulgaris reproduction (p. 61)

Future work on O. vulgaris olfaction must also consider how animals acquire the odours detected by the olfactory organ and what kind of odour the olfactory organ perceives. The OL acting as control centre may be target organ for metabolic hormones such as leptin like and insulin like peptides, and olfactory organ could exert regulatory action on the OL via epigenetic effects of nutrients and pheromones on gene expression (Kohl, 2013; Elekonich and Robinson, 2000).

My comment: The claim by Robinson that “We finally have a mechanism to understand ‘nurture’ in molecular terms…” appears to be an attempt to excuse 20 years of delayed scientific progress. Others have now picked up the slack. They have linked atoms to ecosystems and nurture to nature via epigenetically effected gene expression, and consequently, neural activity and behavior. The molecular mechanisms of cause and effect have been known since 1973 when Dobzhansky claimed:

the so-called alpha chains of hemoglobin have identical sequences of amino acids in man and the chimpanzee, but they differ in a single amino acid (out of 141) in the gorilla. ( p. 127)

See also: Invertebrate behavior – actions or responses?

The uncrowned champions of reducing simple systems even more by eliminating as many confounding factors as possible must be the mollusks. In their riveting, neuron-by-neuron account of how even isolated ganglia of the marine snail Aplysia make spontaneous decisions and incorporate environmental feedback in this process of adaptive behavioral choice, Nargeot and Simmers (2012) elucidate principles of operant conditioning, habit formation, and compulsivity at a level of biological detail that will take decades to reach in most other systems.

See:  Nutrient-dependent/pheromone-controlled adaptive evolution: a model

The honeybee already serves as a model organism for studying human immunity, disease resistance, allergic reaction, circadian rhythms, antibiotic resistance, the development of the brain and behavior, mental health, longevity, diseases of the X chromosome, learning and memory, as well as conditioned responses to sensory stimuli (Kohl, 2012).

My comment: The prediction that it would take decades to detail the links from mollusks to the honeybee model organism to all living genera via conserved molecular mechanisms that link atoms to ecosystems was decades off.

See: Nutrient-dependent pheromone-controlled ecological adaptations: from atoms to ecosystems



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