Mechanical properties such as shape, volume and size affect the dynamics of biological systems. Most of the current methodological approaches are inclined to remove the existence of holes and impurities from systems’ description, regarding them as routes toward mechanical failure. On the contrary, we suggest that the occurrence of holes might be of utmost functional importance, allowing reversible transformations of cellular structures. The focus here is on the widespread occurrence of intracytoplasmic holes, that deeply modifies the topology of living cells and provides researchers with novel operational tools to investigate intracellular dynamics. We take as example the prokaryotic gas vesicles, i.e., intracellular cavities filled with gases spreading from the nearby medium. The mechanical and topological cellular properties dictated by intracytoplasmic holes are investigated, focusing on the physical constraints imposed by their very existence. For instance, the presence of gas vesicles breaks the cytoplasmic homogeneity, leading to inhomogeneity in functional activities and modifications in intracellular flows. Also, a topological approach to cytoplasmic holes suggests novel physiological roles for gas vesicles. For example, the gas vesicles’ ability to increase/decrease cellular volumes provides a mechanism that counteracts the detrimental effects of the surface/volume ratio. In conclusion, a structural/methodological approach based on the occurrence of holes testifies once again how the simple biophysical structure alone can dictate the function.

Instead of the conventional 0 and 1 values, bipolar reasoning uses -1, 0, +1 to describe double-sided judgements in which neutral elements are halfway between positive and negative evaluations (e.g., “uncertain” lies between “impossible” and “totally sure”). We discuss the state-of-the-art in bipolar logics and recall two medieval forerunners, i.e., William of Ockham and Nicholas of Autrecourt, who embodied a bipolar mode of thought that is eminently modern. Starting from the trivial observation that “once a wheat sheaf is sealed and tied up, the packed down straws display the same orientation”, we work up a new theory of the bipolar nature of networks, suggesting that orthodromic (i.e., feedforward, bottom-up) projections might be functionally coupled with antidromic (i.e., feedback, top-down) projections via the mathematical apparatus of presheaves/globular sets. When an entrained oscillation such as a neuronal spike propagates from A to B, changes in B might lead to changes in A, providing unexpected antidromic effects. Our account points towards the methodological feasibility of novel neural networks in which message feedback is guaranteed by backpropagation mechanisms endowed in the same feedforward circuits. Bottom-up/top-down transmission at various coarse-grained network levels provides fresh insights in far-flung scientific fields such as object persistence, memory reinforcement, visual recognition, Bayesian inferential circuits and multidimensional activity of the brain. Implying that axonal stimulation by external sources might backpropagate and modify neuronal electric oscillations, our theory also suggests testable previsions concerning the optimal location of transcranial magnetic stimulation’s coils in patients affected by drug-resistant epilepsy.

Ramsey’s economic theory of saving (RTS) estimates how much of its commodities a nation should save to safeguard the well-being of future generations. Since RTS retains many attractive qualities such as simplicity, strength, breadth and generality, here we ask if it would be useful to investigate biophysical issues. Specifically, we focus on a biological topic that lends itself as a backdrop for the study of the imbalance between intake and expenditure, i.e., the evaluation of the multicellular living organisms’ energetic requirements and constraints. Our problem is to find at each time the optimum distribution and the right balance of the cellular energy budget between consumption and storage: how much must a living organism spare to increase its chances of survival over long periods? Suggesting how to find the optimum allocation of the available energy between expenditure and saving at each time, RTS approaches to biological energy budgets may have a wide range of experimental applications, such as: a) optimization of the long-term survival chances of either immortalized cell cultures, or beneficial bacterial colonies and exogenous probiotic mixtures; b) eradication of detrimental biofilms, such as, e.g., heart valves’ Streptococcus colonies; c) novel anti-stress and anti-ageing strategies.

Ramsey’s theory (RAM) from combinatorics and network theory goes looking for regularities and repeated patterns inside structures equipped with nodes and edges. RAM represents the outcome of a dual methodological commitment: by one side a top-down approach evaluates the possible arrangement of specific subgraphs when the number of graph’s vertices is already known, by another side a bottom-up approach calculates the possible number of graph’s vertices when the arrangement of specific subgraphs is already known. Since natural neural networks are often represented in terms of graphs, we suggest to utilize RAM for the analytical and computational assessment of a peculiar structure supplied with neuronal vertices and axonal edges, i.e., the human brain connectome. We discuss how a RAM approach in neuroscientific issues might be able to locate and trace unexplored motifs shared between different cortical and subcortical subareas. Furthermore, we will describe how notable RAM outcomes, such as the Ramsey’s theorem and the Ramsey’s number, could contribute to uncover still unknown anatomical connexions endowed in neuronal networks and unexpected functional interactions among grey zones of the human brain.

When an edge is removed, a cycle graph Cn becomes a n-1 tree graph. This observation from extremal set theory leads us to the realm of set theory, in which a topological manifold of genus-1 turns out to be of genus-0. Starting from these premises, we prove a theorem suggesting that a manifold with disjoint points must be of genus-0, while a manifold of genus-1 cannot encompass disjoint points.

The unexploited unification of general relativity and quantum mechanics (QM) prevents the proper understanding of the micro- and macroscopic world. Here we put forward a mathematical approach that introduces the problem in terms of negative curvature manifolds. We suggest that the oscillatory dynamics described by wave functions might take place on hyperbolic continuous manifolds, standing for the counterpart of QM’s Hilbert spaces. We describe how the tenets of QM, such as the observable A, the autostates ψa and the Schrodinger equation for the temporal evolution of states, might work very well on a Poincaré disk equipped with rotational groups. This curvature-based approach to QM, combined with the noncommutativity formulated in the language of gyrovectors, leads to a mathematical framework that might be useful in the investigation of relativity/QM relationships. Furthermore, we introduce a topological theorem, termed the punctured balloon theorem (PBT), which states that an orientable genus-1 surface cannot encompass disjoint points. PBT suggests that hyperbolic QM manifolds must be of genus ≥ 1 before measuring and genus zero after measuring. We discuss the implications of PBT in gauge theories and in the physics of the black holes.

Set theory faces two difficulties: formal definitions of sets/subsets are incapable of assessing biophysical issues; formal axiomatic systems are complete/inconsistent or incomplete/consistent. To overtake these problems reminiscent of the old-fashioned principle of individuation, we provide formal treatment/validation/operationalization of a methodological weapon termed “outer approach” (OA). The observer’s attention shifts from the system under evaluation to its surroundings, so that objects are investigated from outside. Subsets become just “holes” devoid of information inside larger sets. Sets are no longer passive containers, rather active structures enabling their content’s examination. Consequences/applications of OA include: a) operationalization of paraconsistent logics, anticipated by unexpected forerunners, in terms of advanced truth theories of natural language, anthropic principle and quantum dynamics; b) assessment of embryonic craniocaudal migration in terms of Turing’s spots; c) evaluation of hominids’ social behaviors in terms of evolutionary modifications of facial expression’s musculature; d) treatment of cortical action potentials in terms of collective movements of extracellular currents, leaving apart what happens inside the neurons; e) a critique of Shannon’s information in terms of the Arabic thinkers’ active/potential intellects. Also, OA provides an outer view of a) humanistic issues such as the enigmatic Celestino of Verona’s letter, Dante Alighieri’s “Hell” and the puzzling Voynich manuscript; b) historical issues such as Aldo Moro’s death and the Liston/Clay boxing fight. Summarizing, the safest methodology to quantify phenomena is to remove them from our observation and tackle an outer view, since mathematical/logical issues such as selective information deletion and set complement rescue incompleteness/inconsistency of biophysical systems.

We suggest that the 14^th century scholar Nicholas of Autrecourt can be regarded as a precursor of the paraconsistent logics developed around 1950. We show how the Sorbonne licentiatus in theology provided in his few extant writings a refutation of both the principle of explosion and the law of non-contradiction, in accordance with the tenets of paraconsistent logics. This paves the way to the most advanced theories of truth in natural language and quantum dynamics.

The dynamical processes of living systems are characterized by the cooperative interaction of many units. This claim enables us to portray the embryo-fetal development of the central and peripheral nervous systems in terms of assemblies of building blocks. We describe how the structure and arrangement of nervous fibers is - at least partially - dictated by biophysical and topological constraints. The far-flung field of soft-matter polymers/nematic colloids sheds new light on the neurulation in mammalian embryos, suggesting an intriguing testable hypothesis: the development of the central and peripheral nervous systems might be correlated with the occurrence of local thermal changes in embryo-fetal tissues. Further, we show a correlation between the fullerene-like arrangement of the cortical microcolumns and the Frank-Kasper phases of artificial quasicrystals assemblies. The last, but not the least, we explain how and why the multisynaptic ascending nervous fibers connecting the peripheral receptors to the neocortical areas can be viewed as the real counterpart of mathematical tools such as knot theory and braid groups. Their group structure and generator operations point towards a novel approach to long-standing questions concerning human sensation and perception, leading to the suggestion that the very arrangement and intermingling of the peripheral nervous fibers contributes to the cortical brain activity. In touch with the old claims of D’Arcy Thompson, we conclude that the arrangement and the pattern make the function in a variety of biological instances, leading to countless testable hypotheses.

Once a wheat sheaf has been sealed and tied up, its packed down straws display the same orientation and zero-divergence. This observation brings us to the mathematical notion of presheaf, i.e., a topological structure in which diverging functions are locally superimposed. We show how the concepts of presheaves and the correlated globular sets, borrowed from category theory and algebraic topology, allow a well-founded mathematical approach to otherwise elusive activities of the brain. The mathematical assessment of brain functions in terms of presheaves: a) explains why spontaneous random spikes synchronize; b) leads to the counterintuitive intuition of antidromic effects in neuronal spikes: when an entrained oscillation propagates from A to B, changes in B lead to changes in A. We provide testable previsions: a) we suggest the proper locations of transcranial magnetic stimulation’s coils to improve the clinical outcomes of drug-resistant epilepsy; b) we advocate that axonal stimulation by external sources backpropagates and alters the neuronal electric oscillatory frequency. Further, we describe how the hierarchical information transmission inside globular sets provides fresh insights concerning different issues at various coarse-grained scales, such as object persistence, memory reinforcement in spite of random noise, Bayesian inferential circuits.

Visual imagery, i.e., the mental experience of an object occurring in the absence of external visual stimulus, might encompass diverse content according to different observers. Further, subjectively experienced time is encoded in the later entorhinal cortex. Starting from these two observations, and considering Einstein’s account of spacetime, we show how, in terms of special relativity, the content of visual imagery is not stationary and fixed, rather depends on the standpoint of the observer. We elucidate how the subjective definition of time (perceived by our mind as static) might give rise to modifications in the length of the imagined object which are experimentally assessable and quantifiable. In particular, based on recent neuroscientific literature, we show how changes in our mental time windows are able to squeeze the visual content of mental imagery.

Dewetting transition - a concept borrowed from fluid mechanics - is a physiological process which takes place inside the hydrophobic pores of ion channels. This transient phenomenon causes a metastable state which forbids water molecules to cross the microscopic receptors’ cavities. This leads to a decrease of conductance, a closure of the hole and, subsequently, severe impairment of cellular performance. We suggest that artificially-provoked dewetting transition in ion channels’ hydrophobic pores could stand for a molecular candidate to erase detrimental organisms, such as viruses, bacteria and cancer cells. We describe a novel type of high-affinity monoclonal antibody, which: a) targets specific trans-membrane receptor structures of harmful or redundant cells; b) is equipped with lipophilic and/or hydrophobic fragments that prevent physiological water flows inside ion channels. Therefore, we achieve an artificial dewetting transition inside receptors’ cavities which causes transmembrane ionic flows discontinuity, channel blockage and subsequent damage of morbid cells. As an example, we describe dewetting monoclonal antibodies targeting the M2 channel of the Influenza A virus: they might prevent water to enter the pores, thus leading to virion impairment.

Causal relationships lie at the very core of our scientific description of biophysical phenomena. Nevertheless, observable facts such as chaotic dynamics, symmetry breaks, long-range collisionless neural interactions, zero-value energy singularities, particle/wave duality, ecological approaches to visual perception elude cause effect inductive explanations. We illustrate how simple topological claims, seemingly useless and far away from scientific inquiry (e.g., “given at least some wind on Earth, there must at all times be a cyclone or anticyclone somewhere”; “if one stirs to dissolve a lump of sugar in a cup of coffee, it appears there is always a point without motion”; “at any moment, there is always a pair of antipodal points on the Earth’s surface with equal temperatures and barometric pressures”) describe a real world, made of projections and mappings unsupplied with causality. Unavoidable, necessary, passive, spontaneous changes in systems’ shapes, dimensions and symmetries incarnate biophysical quantifiable counterparts of abstract mathematical concepts. Real features arising from topological mechanisms do not require causal powers to be produced, because are independent of exerted physical forces, energetic fields’ actions and thermodynamic constraints. Providing examples that shed novel interpretative light on phenomena such as double slit experiments, cellular mechanisms and brain function, we conclude as follows: countless scientific matters can be accessed through methodological weapons which not just break causality, replace temporal correlations and probabilistic a priori knowledge of previous cases, but also permit augments in available information devoid of entropy increases and energy losses.

Geometry deals both with analogical thinking and physical/biological observables. Naïve, common-sense descriptions of objects’ shapes and systems’ trajectories in geometric phase spaces may help experimental investigation. For example, very different biological dynamics, as the developmental growth patterns of the oldest known animal (the extinct Dickinsonia) and the human brain electric oscillations, display a striking analogy: when encompassed in abstract geometric spaces, their paths describe the same changes in curvature: from convex, to flat, to concave and vice versa. This dynamical behavior, anticipated by Nicholas de Cusa in his analogical account of “coincidentia oppositorum” (1440), helps to describe widespread biological paths in the manageable terms of concave, flat and convex curves on donut-like structures. Every trajectory taking place on such toroidal manifolds can be located, through a topological technique called Hopf fibration, into a four-dimensional space. We discuss how the correlation between Hopf fibration and Navier-Stokes equations allows us to treat the above-mentioned biological and neuroscientific curved paths in terms of flows taking place into a viscous fluid medium that can be experimentally assessed and quantified.

We describe cosmic expansion from the standpoint of an observer’s comoving horizon. When the Universe is small, the observer detects a large amount of the total cosmic bits, which number is fixed. Indeed, information, such as energy, cannot be created or destroyed in our Universe, i.e., the total number of cosmic bits must be kept constant, despite the black hole paradox. When the Universe expands, the information gets ergodically “diluted” in our isotopic and homogeneous Cosmos. This means that the observer can perceive just a lower number of the total bits, due the decreased density of information in the cosmic volume (or its surrounding surface, according to the holographic principle) in which she is trapped by speed light’s constraints. Here we ask: how does the second law of thermodynamics enter in this framework? Could it be correlated with cosmic expansion? The correlation is at least partially feasible, because the decrease in the information detected by a local observer in an expanding Universe leads to an increase in detected cosmic thermodynamic entropy, via the Bekenstein bound and the Laudauer principle. Reversing the classical scheme from thermodynamic entropy to information entropy, we suggest that the quantum vacuum’s cosmological constant, that causes cosmic expansion, could be one of the sources of the increases in thermodynamic entropy detected by local observers.

The French-Swiss Professor in inductive philosophy Richard Avenarius (1843-1896), the father of empirio-criticism together with Ernst Mach, is one of the most underrated and misunderstood philosophers ever. It mostly depends upon his terminology, which displays an insurmountable difficulty. However, influenced by the most innovative proposals of his times of transition between the idealistic/rationalist legacies and the new Materialism/scientific interpretation of reality – i.e, by cultural evolutionism, linguistics, biomechanics, entropy/energy and, above all, by the newborn experimental psychology-, he produced a complete system of philosophy and innovative methods of investigation of the laws of knowledge. Hints (chunk, scrap, fragments) of his original ideas can be found not only in philosophers of mind after him - such as Gestalt, phenomenalism, behaviourism, functionalism and cybernetics, autopoiesis, dynamical systems theory, embedded/embodied mind, free-energy principle of the brain – but also in recent neuroscientific theories – nervous transduction, electric spikes, cracking of neural code, multisensory integration -. Our aim is to provide the first chronological English summary of his masterpiece, the “Kritik”, to give the possibility to the (almost) totally unaware English speakers to appreciate such a neglected and innovative thinker.

Physical properties like shape, volume and size affect the dynamics of biological systems. Along these lines, we focus on the topological properties of biological fluids and their biochemical and physiological outcomes. We take as a paradigmatic example the salivary fluid and describe how its topological features may affect the physiopathology of the oral cavity. Topological approaches assess the general properties of saliva, ignoring small-scale physical details such as density, flow rate, stiffness, viscosity. Specifically, the mucin aggregates scattered in the salivary fluid can be tackled in terms of topological holes, i.e., vortical clusters that modify the direction, flow, impulse, local rate-of-change and velocity of saliva. While the current methodological approaches are inclined to remove the effects of impurities assessing systems as homogeneous structures, we argue that the occurrence of mucins breaks up the salivary fluid’s homogeneity, leading to unexpected biophysical modifications. We suggest that every collected salivary sample is not reliable for accurate clinical and experimental investigation, since it displays highly local as well as variable chemical, physical and biological features, not reflecting the current physiological state of the oral cavity. Therefore, the assessment of a single salivary sample is not fully reproducible and cannot provide information about the biophysical, enzymatic and microbiological content of the whole saliva. In sum, the very topological features of the saliva - such as volume, shape, antipodal cells, vortex area, whirling fluid mass, segmentation, discretization, triangulation, node numbering - produce unnoticed biological consequences and network connectivity features with intriguing operational implications.

The central dogma of molecular biology dictates that, with only a few exceptions, information proceeds from DNA to protein through an RNA intermediate. Examining the enigmatic steps from prebiotic to biological chemistry, we take another road suggesting that primordial peptides acted as template for the self-assembly of the first nucleic acids polymers. Arguing in favour of a sort of archaic “reverse translation” from proteins to RNA, our basic premise is a Hadean Hearth where key biomolecules such as amino acids, polypeptides, purines, pyrimidines, nucleosides and nucleotides were available under different prebiotically plausible conditions, including meteorites delivery, shallow ponds and hydrothermal vents scenarios. Supporting a protein-first scenario alternative to the RNA world hypothesis, we propose the primeval occurrence of short peptides termed “selective amino acid- and nucleotide-matching oligopeptides” (henceforward SANMAOs) that noncovalently bind at the same time the polymerized amino acids and the single nucleotides dispersed in the prebiotic milieu. We describe the chemical features of this hypothetical oligopeptide, its biological plausibility and its virtues from an evolutionary perspective. We provide a theoretical example of SANMAO’s selective pairing between amino acids and nucleosides, simulating a poly-Glycine peptide that acts as a template to build a purinic chain corresponding to the glycine’s extant triplet codon GGG. Further, we discuss how SANMAO might have endorsed the formation of low-fidelity RNA’s polymerized strains, well before the appearance of the accurate genetic material’s transmission ensured by the current translation apparatus.

Intestinal gases are usually discarded as physiologically inert, useless sub-products of colonic fermentation that must be expelled to prevent discomfort and meteorism. Starting from the observation that many living beings use exogenous and/or endogenous gases to attain evolutionary benefits, we question whether intestinal gases in healthy humans could have underestimated physiological effects, either intestinal or extra-intestinal. We examine gaseous volume, composition, source and local distribution in proximal as well as distal gut, providing extensive data that may serve as reference for future studies. We analyze each one of the most abundant intestinal gases and describe their diffusive patterns, active trans-barrier transport dynamics, chemical properties, intra-/extra-intestinal metabolic effects mediated by intracellular, extracellular, paracrine and distant actions. Discussing the physical properties of the whole intestinal gaseous mixture, we illustrate how changes in volume/pressure can be generated by two different mechanisms, namely, physical muscular gut contraction and biological colonic fermentation, with quite different metabolic outcomes. The experimental gas laws suggest that the gaseous exchanges between lumen and bloodstream are impaired by muscular contraction and improved by muscular relaxation. In turn, the surface-area-to-volume ratio suggests that the gaseous exchanges are impaired by microorganismal overproduction and improved by microorganismal reduction. Further, theoretical stochastic approaches from probability theory indicate that the non-turbulent, random paths of gas molecules inside colonic haustra do not homogenously spread over the whole mucosal surface. This means that the intestinal area available for lumen/blood metabolic exchanges is much less than expected not just in disease states, but also in healthy individuals.

Neuroscientists are able to detect physical changes in information entropy in available neurodata. However, the information paradigm is inadequate to fully describe nervous dynamics and mental activities such as perception. This paper provides an effort to build explanations to neural dynamics alternative to thermodynamic and information accounts. We recall the Banach–Tarski paradox (BTP), which informally states that, when pieces of a ball are moved and rotated without changing their shape, a synergy between two balls of the same volume is achieved instead of the original one. We show how and why BTP might display this physical and biological synergy meaningfully, making it possible to tackle nervous activities. The anatomical and functional structure of the central nervous system’s nodes and edges allows to perform a sequence of moves inside the connectome that doubles the amount of available cortical oscillations. In particular, a BTP-based mechanism permits scale-invariant nervous oscillations to amplify and propagate towards far apart brain areas. Paraphrasing the BPT’s definition, we could state that: when a few components of a self-similar nervous oscillation are moved and rotated throughout the cortical connectome, two self-similar oscillations are achieved instead of the original one. Furthermore, based on topological structures, we illustrate how, counterintuitively, the amplification of scale-free oscillations does not require information transfer.

Physical measurements might display range values extending towards infinite. The occurrence of infinity in physical equations, such as the black hole singularities, is a troublesome issue that causes many theories to break down when assessing extreme events. Different methods, such as re-normalization, have been proposed to avoid detrimental infinity. Here a novel technique is proposed, based on physical geometrical considerations and the Alexander Horned sphere, that permits to undermine infinity in physical equations. In this unconventional approach, a continuous monodimensional line becomes an assembly of countless bidimensional lines that superimpose in quantifiable knots and bifurcations.

During the exploration of the surrounding environment, the brain links together external inputs, giving rise to perception of a persisting object. During imaginative processes, the same object can be recalled in mind even if it is out of sight. Here, topological theory of shape provides a mathematical foundation for the notion of persistence perception. In particular, we focus on ecological theories of perception, that account for our knowledge of world objects by borrowing a concept of invariance in topology. We show how a series of transformations can be gradually applied to a pattern, in particular to the shape of an object, without affecting its invariant properties, such as boundedness of parts of a visual scene. High-level representations of objects in our environment are mapped to simplified views (our interpretations) of the objects, in order to construct a symbolic representation of the environment. The representations can be projected continuously to an environmental object that we have seen and continue to see, thanks to the mapping from shapes in our memory to shapes in Euclidean space.

Starting from unidentified objects moving inside a two-dimensional Euclidean manifold, we propose a simple method to detect the topological changes that occur during their reciprocal interactions and shape morphing. This method, which allows the detection of topological holes development and disappearance, makes it possible to solve the uncertainty due to disconnectedness, lack of information and absence of objects’ sharp boundaries, i.e., the three troubling issues which prevent scientists to select the required proper sets/subsets during their experimental assessment of natural and artificial dynamical phenomena, such as fire propagation, wireless sensor networks, migration flows, neural networks’ and cosmic bodies’ analysis.

Here we show how a recently-introduced method from algebraic topology, namely proximal planar vortex 1-cycles, might be helpful in detecting hidden features of the shapes and holes in images, therefore contributing to the solution of both cold and fresh forensic cases. In particular, we test the efficacy of this technique by assessing one of the most puzzling cases of recent history, i.e., Aldo Moro’s death. Terrorists of the Red Brigades claimed that they killed Moro when he was placed inside the trunk of a car,shooting him with a barrage of bullets. We demonstrate, based on the analysis of the photographs taken during the autoptic procedure, that the terrorist’s account does not hold true. Our results, showing different series of shots, point towards a three-step execution, with the first phasestaking place outside the car. In conclusion, the novel forensic analysis method introduced in this paper permits the evaluation of a collection of vortex cycles/nerves equipped with a connectedness proximity, which makes it possible to assess unexpected spatial clusters in photographs.

The entangled antipodal points on black hole surfaces, recently described by t’Hooft, display an unnoticed relationship with the Borsuk-Ulam theorem. Taking into account this observation and other recent claims, suggesting that quantum entanglement takes place on the antipodal points of a S³ hypersphere, a novel framework can be developed, based on algebraic topological issues: a feature encompassed in an S² unentangled state gives rise, when projected one dimension higher, to two entangled particles. This allows us to achieve a mathematical description of the holographic principle occurring in S². Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a four-dimensional spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a negative mass might exist on the surface of a black hole.

Starting from the tenets of human imagination, i.e., the concepts of lines, points and infinity, we provide a biological demonstration that the skeptical claim “human beings cannot attain knowledge of the world” holds true. We show that the Euclidean account of the point as “that of which there is no part” is just a conceptual device, untenable in our physical/biological realm: terms like “lines, surfaces and volumes” label non-existent, arbitrary properties. We also elucidate the psychological and neuroscientific features hardwired in our brain that lead us humans to think to points and lines as truly occurring in our environment. Therefore, our current scientific descriptions of objects’ shapes, graphs and biological trajectories in phase spaces need to be revisited, leading to a proper portrayal of the real world’s events. In order to provide also a positive account, we view miniscule bounded physical surface regions as the basic objects in a biological context in a traversal of spacetime instead of the usual Euclidean points. Our account makes it possible to erase a painstaking problem that causes many theories to break down and/or being incapable of describing extreme events: the unwanted occurrence of infinite values in equations, such as singularity in the description of black holes. We propose a novel approach, based on point-free geometrical standpoints, that banishes infinitesimals and leads to a tenable physical/biological geometry. We conclude that points, lines, volumes and infinity do not describe the world, rather they are fictions introduced by ancient surveyors of land surfaces.

The unexploited unification of general relativity and quantum physics is a painstaking issue that prevents physicists to properly understanding the whole of Nature. Here we propose a pure mathematical approach that introduces the problem in terms of group theory. Indeed, we build a cyclic groupoid (a nonempty set with a binary operation defined on it) that encompasses both the theories as subsets, making it possible to join together two of their most dissimilar experimental results, i.e., the commutativity detectable in our macroscopic relativistic world and the noncommutativity detectable in the quantum, microscopic world. This approach, combined with the Connes fusion operator, leads to a mathematical framework useful in the investigation of relativity/quantum mechanics relationships.

Turbulence is a fluid dynamic problem refractory to mathematical treatment. Examining a theoretical model of liquid water flowing in a cylinder at different Raleigh numbers, we propose a novel approach to elucidate the first stages of turbulent flows. The weakly bonded molecular assemblies of liquid water form a fluctuating branched polymer in which every micro-cluster displays different density. Against the common view of liquid water as an incompressible and continuous fluid, we suggest that the occurrence of transient local aggregates could be able to generate the vortices and eddies that are the hallmarks of turbulence. We quantify the local changes in velocity, diameter and density required to engender “obstacles” to the average flow. Then, we show how these microstructures, equipped with different Raleigh numbers and characterized by high percolation index, could generate boundary layers that contribute to micro-vortices production. We conclude that the genesis of turbulence cannot be assessed in terms of collective phenomena, rather is sustained, among many other factors, by the underrated microscopic inhomogeneities of fluids like liquid water.

The brain, rather than being homogeneous, displays an almost infinite topological genus, because is punctured with a very high number of topological vortexes, i.e., .e., nesting, non-concentric brain signal cycles resulting from inhibitory neurons devoid of excitatory oscillations. Starting from this observation, we show that the occurrence of topological vortexes is constrained by random walks taking place during self-organized brain activity. We introduce a visual model, based on the Pascal’s triangle and linear and nonlinear arithmetic octahedrons, that describes three-dimensional random walks of excitatory spike activity propagating throughout the brain tissue. In case of nonlinear 3D paths, the trajectories in brains crossed by spiking oscillations can be depicted as the operation of filling the numbers of the octahedrons in the form of “islands of numbers”: this leads to excitatory neuronal assemblies, spaced out by empty area of inhibitory neuronal assemblies. These procedures allow us to describe the topology of a brain of infinite genus, to assess inhibitory neurons in terms of Betti numbers, and to highlight how non-linear random walks cause spike diffusion in neural tissues when tiny groups of excitatory neurons start to fire.

The Universe, rather than being homogeneous, displays an almost infinite topological genus, because it is punctured with a countless number of gravitational vortexes, i.e., black holes. Starting from this view, we aim to show that the occurrence of black holes is constrained by geometric random walks taking place during cosmic inflationary expansion. At first, we introduce a visual model, based on the Pascal’s triangle and linear and nonlinear arithmetic octahedrons, which describes three-dimensional cosmic random walks. In case of nonlinear 3D paths, trajectories in an expanding Universe can be depicted as the operation of filling the numbers of the octahedrons in the form of “islands of numbers”: this leads to separate cosmic structures (standing for matter/energy), spaced out by empty areas (constituted by black holes and dark matter). These procedures allow us to describe the topology of an universe of infinite genus, to assess black hole formation in terms of infinite Betti numbers, to highlight how non-linear random walks might provoke gravitational effects also in absence of mass/energy, and to propose a novel interpretation of Beckenstein-Hawking entropy: it is proportional to the surface, rather than the volume, of a black hole, because the latter does not contain information.

Relationships among near set theory, shape maps and recent accounts of the Quantum Hall effect pave the way to quantum computations performed in higher dimensions. We illustrate the operational procedure to build a quantum computer able to detect, assess and quantify a fourth spatial dimension. We show how, starting from two-dimensional shapes embedded in a 2D topological charge pump, it is feasible to achieve the corresponding four-dimensional shapes, which encompass a larger amount of information. This novel, relatively straightforward architecture not only permits to increase the amount of available qbits in a fixed volume, but also converges towards a solution to the problem of optical computers, that are not allowed to tackle quantum entanglement through their canonical superposition of electromagnetic waves.

The unexploited unification of quantum physics, general relativity and biology is a keystone that paves the way towards a better understanding of the whole of Nature. Here we propose a mathematical approach that introduces the problem in terms of group theory. We build a cyclic groupoid (a nonempty set with a binary operation defined on it) that encompasses the three frameworks as subsets, representing two of their most dissimilar experimental results, i.e., 1) the commutativity detectable both in our macroscopic relativistic world and in biology; 2) and the noncommutativity detectable both in the microscopic quantum world and in biology. This approach leads to a mathematical framework useful in the investigation of the three apparently irreconcilable realms. Also, we show how cyclic groupoids encompassing quantum mechanics, relativity theory and biology might be equipped with dynamics that can be described by paths on the twisted cylinder of a Möbius strip.

Collective spread of aggregated viral particles may have beneficial effects on viral capability to survive in the external environment, to counteract immune responses, and to successfully colonize host cells. Here we ask whether SARS-Cov-2 particles, responsible for COVID-19, display collective clustering behavior. Looking at microphotographs and movies of SARS-Cov-2 particles emerging from the surface of cultured cells, we describe single virions that tend to aggregate in progressively larger globular assemblies, until a network-like appearance is achieved. When SARS-Cov-2 particles stick into each other, the squeezing of single virions leads to improved viral package in host’s fluids. We discuss how these findings might explain both the ability to spread of SARS-Cov-2 and the clinical severity of COVID-19 in humans, paving the way to novel therapeutic strategies to mechanically disrupt collective clustering.

The internationals guidelines about food intolerances, allergy and immunity provide for rigorous steps in which ultrasonography is not provided. However there is evidence in literature about an ancillar role of ultrasonography in these conditions. In this report we analyze the main pathologies with allergic or immune pathogenesis