Plant Genomics and Developmental Biology Consultant & Expert




Bohm and Inner-Ordered Mutation: A Perspective on Biology and Physics, with Views on Statistics and Discontinuity



   All of reality can be ordered levels of reality, and there can be an infinite number of such levels. These are in a dynamic plenum, flowing from and through each other, and generating an explicate order, which is the reality currently addressed by science. And this would include quantum mechanics.  This view of existence was developed by the theoretical physicist, David Bohm (e.g., Bohm, 1980). In 1967, he took part in a symposium, organized by the developmental biologist, C. H. Waddington, in which, Bohm presented, in part, this theoretical view, based on his own investigations into quantum mechanics. In those investigations, Bohm strove to demonstrate an underlying level of order to quantum phenomena, manifesting as an underlying and hidden determinism or deterministic potential of implicate orders, which unfold into an explicate order. Quantum mechanics, manifests randomness and discontinuity because it is especially incomplete at this micro level of the explicate order.  Statistics is applied in order to provide a less incomplete view of quantum behavior. In doing so, it does not address or overlooks specificity. Grasping such  complementing specificity would enable a less incomplete view in research. Continuity exists throughout the ordered implicate levels. Such levels are themselves ordered in hierarchies.

 In this symposium, Bohm addressed biological issues in the context of a reality of orders, which are enabled by a unifying, implicit continuity. He postulated that mutation in organisms and within evolution are not random but follow an inner ordering as reflected and enfolded dynamically through the orders of reality. Such an inner ordering of mutation would be a necessary component of evolution, he proposed. As Bohm states in this regard:

 One observation that could be relevant would be to trace a series of successive mutations to see if the order of changes is completely random....There may be a tendency to establish a series of similar changes [mutations] or differences that would constitute an internally ordered process of evolution... in which mutations [in a transitional species] tend to be fairly  rapid and strongly directed in some order... If such deviation from randomness could be found, this could have very far-reaching consequences. For it would imply that when a given type of change [or mutation] has taken place, there is is an appreciable tendency in later generations for  a series of similar changes to take place. Thus, evolution would tend to get 'committed' to certain general lines of development. Of course, survival in the total natural environment would ultimately decide  which lines could be sustained. Nevertheless, an entirely different principle of internal order would determine both the nature of these 'lines' and how they would tend  to vary and transform into other 'lines' (Bohm, 1969).

In 1967, it was postulated by the author that evolution has occurred through the controlled, directed mutation of genes. This control was due  to genetic mutators, which enhanced  the degrees of mutagenesis and the timing of such, giving such mutagenesis developmental features and providing evolution with an inner, non-random parameter (Lieber, 1967).  Subsequent, published research by the author gave repeated support to  the view that mutation has developmental features, such as spatial-temporal control at various genomic levels of organization. And thereby, such inner, developmental control at different levels would have provided evolution with an inner-order of non-randomness (Lieber, 1972,  1975, 1976, 1989, 1996, 1998b, 1998c, 2000, 2001 2011, 2016, and 2019.) This gives a strong credibility, from the stand point of the biological scale or order of reality, to Bohm's theoretical position.

Temporal control or temporality appears to be a significant feature of biological phenomena at various scales, as C.H. Waddington points out in reviewing the commonalities of the articles presented in the 1967 symposium. This suggested a way to present or unify a theoretical biology (Waddington, 1969). Such temporality is clearly evident in the genetic control of mutation, which generates a ordered, programmed mutagenesis. As pointed out by the author, the genetic control of mutation in response, adaptively, to environmental stresses may provide a unifying insight into all biological processes, suggesting a unifying principle of ultimate order and coherence in the universe (Lieber, 1998a, 1998b, and 2016). Temporality, its unfolding, would be a feature of such order. This would be a view similar to that of Bohm's.  A unified, theoretical biology, circumventing a total statistical approach, could arise from such views, which may provide  further insights into physics. A sole statistical approach would be limiting.

 Even so, statistics has played a significant role in biological investigations, especially with regard to studies of mutation. A statistical methodology was brought to bear on the study of  inner-controlled mutation at the karyotypic level in a colonial fungus (Lieber, 1972, 1976). In the colonial, green fungus, Aspergillus nidulans of a particular constructed strain, programmed mutator phenomena in many  green colonies were made evident in the groups of colonies. These colonies had two karyotypic mutators that interacted with one another in such a manner  as to produce temporally, controlled mutations, manifested phenotypically as yellow sectors. (For a picture of one such colony, see Figure 7 on the first page of this website.) These colonies were studied using statistical methodologies. Many of the colonies exhibited  controlled mutation frequencies very similar to one another. Yet, some  other colonies in the same experimental group had reduced mutation frequencies, and those mutations were not so ordered. However, such statistics did not reveal certain information as to what caused some colonies to exhibit a difference in mutation frequency and pattern from that of the high mutation producers, a few differences being major. In other words, the statistical methodologies did not reveal the  cause  or dynamic for variations in the degrees of such mutator phenomena between colonies composing each sub-group. The statistics revealed only information for any group of colonies as a whole regarding the most likely global effects of the mutators. Of course, likely explanations were postulated, many pertaining to the known genetic instability of one of the mutators itself.  However, the statistics did not inform one of the pattern of such instability, nor its temporal occurrence.

 In subsequent studies, colonial mutator strains derived indirectly from cultures stored for a significant period in cool temperatures displayed lower, less programmed mutation frequencies when such were grown at culture-growing temperatures. Some, in that group produced  relatively higher frequencies of mutations or mutant sectors than other colonies in that group. (See an example of one such colony at the end of this article.) Again, statistics did not provide insights for such differences in mutation frequencies. Also, though of the same strain, the colony pictured below differed from the colony in Figure 7 in mutation frequency and in the pattern of such mutations, as noted by observing the mutant yellow sectors produced by the respective colonies.

Why would this be the situation? The statistics applied to this specific situation did not provide insights. Yet, non-statistical based postulates were made. These pertained to age of cultures and the possible influence of high temperature. These postulates were supported through a change and broadening of experimental protocols. Only through young cultures (colonies) of fungi, derived from newly generated spores, grown at high temperatures, were very high, programmed mutations generated again in a highly programmed manner within such colonies. There was very little variation in frequencies from colony to colony. This could be  inferred from the statistical data and significance tests involving experimental and control groups of colonies. The high temperature, or high infrared radiation, acted, it was concluded, as a non-local agent in the promotion of a high degree of programmed mutation within the experimental colonies.

 The change in experimental protocols thus made evident a new cause pertaining to or influencing genetic control. However, the statistical method did not address or explain this, and an epigenetic explanation was given that again circumvented statistics (Lieber, 1972, 1976, 1998b, 2016; also, see articles on this website.) Again, the explanatory power of statistics is shown to be limited. Nevertheless, the designing of new experiments through the application of mind enabled the detection of a further cause (or causes), thereby negating the appearance of randomness, or apparently random specifics, through the agency of the revised experimental protocols. And because of such, through changing protocols, enabled by the human mind, a growing, more complete view has been enabled. And such a new experimental view, enabled through the human mind, has thus circumscribed the limitations of statistics, (itself a creation of the human mind), limitations which appear to be due to uncontrolled specifics or random specificity beyond a certain level or scale, and which are tied to a specific experimental method or design. The human mind can nevertheless circumvent the limitations of its own approaches to nature, but ironically, it is bound to them when accepting a priori a limitation of our knowledge of nature, due to our generally not accepting the limitations of this knowledge's mathematical tool or methodology.

 This limitation of this tool when addressing biological nature is analogous, if not similar, to the statistical investigations in quantum mechanics. Such statistics is based, for example, on studies of the behavior of large numbers electrons or the behavior of large numbers of atoms exhibiting radioactivity. The statistics does not provide information  as to behavior of an individual electron as far as its trajectory or path is concerned, or, when and why an individual atom becomes radioactive. The statistics does not address causation at that level. In fact, it precludes an awareness of such causation or an ordering, integrating process. As Einstein indicated, such statistical limitation makes quantum mechanics itself unable to present a complete view of reality. The implication would be that quantum mechanics is incomplete. This is a position that Einstein held through the years. As Albert Einstein wrote on this subject in 1949 :

What does not satisfy me in that theory [of quantum mechanics], from the standpoint of principle, is its attitude towards that which appears to be the programmatic aim of all physics: the complete description of any (individual)  real situation...One arrives at very implausible  theoretical conceptions, if one attempts to maintain the thesis that the statistical quantum theory  is in principle capable of producing a complete description of an individual physical system. On the other hand, those difficulties of theoretical interpretation disappear, if one views the quantum-mechanic description as the description of ensembles of systems...Within the framework of statistical quantum theory there is no such thing as a complete description of the individual system (Einstein, 1949).

In studying biological processes and quantum phenomena, statistical studies leave out significant information pertaining to the behavior of specific structures and processes. Though biology and quantum mechanics operate on vastly different  scales, they display the same  lack of accessibility to the causes of deeper, specific phenomena through a statistical approach. Within both scales, the accessibility to causation at a specific level becomes precluded. As with quantum mechanics, biological knowledge is also incomplete, lacking a unifying  concept or perspective as to underlying dynamics that connect specific situations. David Bohm and this author have attempted, through their respective and similar theories and approaches, to circumvent this problem and to show that reality with its various features is dynamically and coherently unified through all scales. And thereby, it can be accessed more completely through new experimental approaches and a flexible application of reason. This would bring us towards completion in our knowledge of quantum mechanics and biology. As Bohm stated:

More generally, what is needed, in physics as well as in biology, is to perceive the existing facts anew, in the light of the notion of order, and of a hierarchy of orders. Such perception will evidently tend to lead us to ask new questions in our scientific research (Bohm, 1969).

The limitation of statistical approaches could thus be circumvented in physics and biology. A new paradigm could eventually ensue. This new paradigm would recognize that our access to reality is not complete, but can become progressively less incomplete. This would be so because  the explicate reality is itself  undergoing varied completion dynamics, and we are part of those dynamics. The completion dynamic would be restricted because the  unfolding of the processes of an implicit, implicate reality into an explicate realty, the reality of science, are not completely simultaneous, as noted by Bohm in later publications, precluding our current methodologies from overcoming such at present. Yet, recognizing such a joined duality of the implicate and explicate orders, through increasingly completing dynamics, and the human mind's participation in this, making causation more and more evident, could lead to new conceptual and methodological approaches that would circumvent (or make unnecessary) a statistical approach, at least for the most part. For example, significance testing does provide important information. And which, in my own biological research, such supported important hypotheses.

Because this explicate order is not  totally complete, and not completely accessible through current methodologies, according to Bohm, it has features of  apparent discontinuity. This enables the appearance of randomness and thus the application of statistics to make a disconnected appearance less incomplete, and thereby, fuller. Such discontinuity appears to be due to (or manifest) the fractural nature of our explicate order or existence, which is also vortical in its design (Lieber, 2023). Fractals are self-similar structures or designs that exist across different scales or levels of organization, and which may even extend into the implicate order of existence.  An example of a universal, self-similar fractal occurring in nature is the generative logarithmic spiral. And such a spiral generates continuity as well  as discontinuity. In fact, it is a situation where discontinuity emerges from continuity. For example, the curves of a special yet universal logarithmic spiral generated over 90 degrees are disconnected with respect to one another when viewed along their increasing radii; but, they are connected or continuous to one another through the growth of the self-similar spiral. Moreover, the increased sizes of the curves, as measured by their radii, are in a constant growth proportion with respect to one another. This proportion is 1.618, the golden ratio of constant proportional growth in many organisms.

Thus, continuity determines or generates discontinuity. This geometrical perspective applied to quantum mechanics indicates that the apparent discontinuity of quantum or energy states is ultimately due to an underlying or implicit generative continuity displayed through a vortical, fractal design or structure. (Also, see Lieber, 2023.) For example, the different  energy levels of electron orbitals in an atom are in discontinuity with  respect to one another. However, they can also be the continuous, vortical energy curves of a vortically structured atom. Vortical atoms manifest a vortical reality (Lieber, 1998a, 2021, 2023). Also, through the intersections of vortical continuities, discontinuity, as quantization, also becomes manifest (Lieber, 1998a, 2021). Discontinuity thus becomes fracturalization and intersection, which appears to be the  inherent reality of the micro-realm and of various features of the macro-realm, such as missing or uncontrolled specificities, which current experimental protocols necessarily allow.

 Nevertheless, such discontinuity is not an absolute structure of existence, whatever scale, but a contingent, emergent feature of an unifying, underlying generative continuity (or continuities), which is  represented by a generative logarithmic spiral of generated continuity, and which is enabled through a constant growth rate of the golden ratio, a universal constant. This  generative continuity or constancy present in reality has become seized by the human mind, and thereby has enabled scientific progress by making more and more evident new dynamic causes, and thereby less and less randomness. For the future, through the application of this universal constant via new research approaches, enabled by an evolving or unfolding human mind, would a new paradigm arise. This would allow scientists to grasp, comprehend, and make evident more completely, and to better control to a point, the generative, stable, interconnected specificities within the continuities of existence, whereby randomness, or random specificity, becomes a limiting case at best.

Such control through experimental methodologies would not be totally enabled because of the immutable universals being embedded through the specifics of reality. This was a position presented by Paul Lieber to account for experimental protocols  not being able to provide a certain view, but only a statistical view, of reality, especially that of quantum behaviour. However, the human mind has also immutable features joined to the universals, and this has enabled us to progressively access such causal interconnections between specificities and the completion dynamics of the universe. And, through such access, humans have been enabled to gain progressive control of  many of reality's specifics, as made evident by technology.





    A dual mutator strain of Aspergillus nidulans. This colony was derived from newly generated spores produced by a newly generated green sector of improved growth rate and smooth morphology. That sector emerged from a colony obtained from spores produced by a colony that was stored in a cold room for a significant period. Other colonies were obtained from the spores of other, newly generated green sectors, but those colonies produced far less yellow sectors. One could also ask why this colony displayed a mutation pattern different from the one in Figure 7, even though the above colony is of the same strain as the colony in Figure 7. And both were cultured at the same temperature. Yet, the statistics precludes any idea of a cause. The white sectors are endemic to colonies of the dual mutator strain, as inferred from statistical data, but not the reason or cause of such. See the article on evolution in this website for more detailed information about the Aspergillus strains involved and their histories.




Bohm, D. (1969). Some remarks on the notion of order. Towards a Theoretical Biology Number 2. Sketches. pp: 18-40. Edited by C. H. Waddington. Aldine Publishing Company, Chicago.

Bohm, D. (1980). Wholeness and the Implicate Order.  London and Boston: Routledge and Kegan Paul , Publishers.

Einstein,  A. (1949). Remarks concerning the essays brought together in this co-operative volume. Albert Einstein Philosopher-Scientist Volume Two. pp: 665-688. Edited by Paul Author Schilpp. Open Court and Cambridge University Press.

Lieber, M. (1967). Mutation, Development and Evolution. Thesis. Institute of Animal Genetics, University of Edinburgh.

Lieber, M. (1972). Environmental and genetic factors affecting instability at mitosis in Aspergillus nidulans. Ph.D. Thesis, University of Sheffield.

Lieber, M. (1975). Environmental and genetic factors affecting chromosomal instability at mitosis and the importance of chromosomal instability in the evolution of developmental systems. Evolution Theory 1: 97-104.

Lieber, M. (1976). The genetic instability and mutagenic interaction of chromosomal duplications present together in haploid strains of Aspergillus nidulans, Mutation Res. 37: 33-66.

Lieber, M. (1989). New developments on the generation of mutations in Escherichia coli lysogens. Acta Microbiologica Hungarica 36(4): 377-413.

Lieber, M. (1990). Mutagenesis as viewed from another perspective, Riv. Bio./B. Forum 83 (4): 513-522.

Lieber, M. (1998a) The Living Spiral.  A Dimensionless Biological Constant Gives a New Perspective to Physics.  Rivista di Biologia/Biology Forum, vol 91 , no. 1, 91-118. View Abstract PDF  [Back] 

Lieber, M. (1998b). Environmentally responsive mutator systems: toward a unifying perspective, Riv.Biol./B. Forum 91: 425-458.

Lieber, M. (1998c). Hypermutation as a Means to Globally Re-Stabilize the Genome Following Environmental Stress. Mutation Research, Fundamental and Molecular Mechanisms of Mutagenesis, vol. 421 , no. 2, 219-220.

Lieber, M. (2000).  Adaptively Responsive Hypermutation and Its Configurational-Based Regulation Due to Global Position Effect. Mutation Research, Fundamental and Molecular Mechanisms of Mutagenesis, vol. 449 , nos. 1 & 2, 57-60.

Lieber, M. (2001). Temporal control of environmentally responsive hypermutation involving cryptic genes. Mutation Research 473: 255-257.

Lieber, M. (2011). The problem of antibiotic resistant bacteria. The important role of environmentally responsive mutagenesis, its relevance to a new paradigm that may allow a solution. Theoretical Biology Forum. 104, No. 1: 91-102.

Lieber, M. M. (2016). Toward a New Paradigm for the Evolution of Developmental and Growth-Pattern Systems in Plants and Animals, Plant Growth, Professor Everlon Rigobelo (Editor). IntechOpen. DOI: 10.5772/64785

Lieber, M. M. (2019). The Induction and Maintenance of In Vitro Plant Morphogenesis as Viewed from a New Perspective, with Theoretical and Constructive Implications. BioSystems, 184: 1-7.

Lieber, M. M. ( 2021). Cosmos and History: The Journal of Natural and Social Philosophy. Vol. 17 (3): 365-396.

Lieber, M. M. ( 2023). Cosmos and History: The Journal of Natural and Social Philosophy. Vol. 19 (1): 21-62.

Waddinton, C. H. (1969). Comments by C. H. Waddington. Towards a Theoretical Biology Number 2. Sketches. pp: 265-267. Edited by C. H. Waddington. Aldine Publishing Company, Chicago.





                                     Copyright (c) by Michael Lieber