Topology, the foundation of science

--- An overview of laws of life, physics, and mathematics

Copyright © February 1996 by Dr. Tienzen (Jeh-Tween) Gong

I: Introduction

Life is the manifestation of all Nature laws, physics, mathematics and all the whatnot.

Looking at every multicellular life form, many questions arise.

The interplay between body shapes and genes involve Topology. The interaction between development and space-time involve physics. The driving master (whatever or whoever that is) or the free will is definitely some sorts of intelligence. These issues obviously involve philosophy, metaphysics, mathematics, physics and theology, but unfortunately the life science is so far confined mainly in Embryology, Molecular Biology and Genetics. In fact, all above questions can be understood, addressed and answered without the nitty-gritty knowledge of genetics or molecular biology. This paper intends not only to address all above questions with common language (no technical knowledge on molecular biology and genetics required) but to provide a unified scheme between all disciplines (mathematics, physics, theology, biology).

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II: The initial signal for cell differentiation --- Geometry

The early development of a life is played out in three stages.

During the cleavage period, all cells are equivalent (not differentiated). In fruitfly (Drosophila) experiment, a male cell was induced into a female embryo to form a gynandromorphs (an individual with male and female halves) during the cleavage period, and the mixtures of male and female parts in the adult is somewhat random. That is, the cell fate is not assigned during the cleavage.

During the blastula stage, cells are differentiated, and this differentiation depends on the location of each cell in the blastula. The ventral part of blastula will become the internal organs. Furthermore, this initial differentiation is still reversible at this stage if cells are moved to a different location. The dorsal (back) of the blastula (the hollow ball) will become the outer layer during the gastrulation and will give rise to nerve system. However, their definite differentiation will not take place until they come in contact with another region, one of mesodermal (inner layer) origin.

This very important life process, so far, does not need to be described in terms of molecular biology or genetics. It is simply transformations of geometry: from a single cell to a solid ball (Morula); from a solid ball to a hollow ball (Blastula); from a hollow ball to a tube (or a donut). It is the geometrical addresses which give rise to the cells differentiation. It is the geometrical contact which assigns the cell fates. My paper --- How to reach Ultimate Reality in a finite number of steps in terms of sciences (presented at 19th World Congress of Philosophy in Moscow 1993 and again at 8th Biennial Meeting of the International Society for the Study of Human Ideas on Ultimate Reality and Meaning at University of Toronto 1995) --- provides a unified scheme between Topology, physics, mathematics and life with the concept of ball-donut transformation.

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III: The active actors of life --- time and space

The active actors of life in the eyes of all life scientists (molecular biologists, geneticists, etc.) are genes, enzymes, proteins, and perhaps, those actors play the life drama on the stage of space and time. No one ever see space and time themselves as the active actors (driving forces) of life.

Every egg has a topological (or geometrical) structure and is, in general, asymmetric. Although different experiments (acts of external intervention) are able to alter the axes of the embryo (which end as head or tail), the shape of the egg do correlates with the axes of the embryo in wild when there is no external intervention.

In the case of fruitfly, the body plan is controlled initially by four morphogenic gradients. Morphogen is a substance which determines the local pattern of differentiation. In order to make a head, the head genes (bicoid) must be present at the place that a head is going to be, and they shall not be (at least not in high concentration) at any other places. Otherwise, there will be heads everywhere. This is achieved in following ways.

Therefore, the body plan of the fruitfly (or any multicellular life) is constructed (or determined) by four factors:

  1. A topological and chemical polarized structure;
  2. Genes of each organ (head, tail, etc.);
  3. The half-life of each gene;
  4. The geometrical separation (space) between the genes.

In short, for the body development, time, space and geometry are controlling managers, and genes are only blue collar workers.

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IV: The interaction between past, present, and future

The body development is controlled by a temporal hierarchy of genes. There are two types of veto genes in this temporal hierarchy.

The sex chromosomes present in the fertilized ovum are handed down through many generations of cell division to all cells of the body. Thus, every cell, whether in the liver, the muscles, or the brain, has information defining its own sex, which is the same as the sex of the entire organism. However, the sex-determining gene TDF (Testis-Determining Factor) works only in one tissue, the gonad. Between the fifth and seventh week after fertilization, human embryos of either sex develop an all-purpose gonad that can later become either a testis or an ovary. If TDF (male sex gene) is blocked or switched off in anyway, the gonad waits until the thirteenth week and then begins developing as an ovary, and he becomes a girl.

If he does get a testis and if it does produce the hormone testosterone (or androgens) in the eighth week of gestation, then some all-purpose embryonic structures develop into penis and scrotum. But, if he has a defective testosterone receptor (developed not by sex gene), then his all-purpose embryonic structures will develop into clitoris, labia and vagina while his testes are buried in the groin or labia. This kind of pseudohermaphrodites are often beautiful girls, and many cases have turned up among female fashion models.

In laboratory experiments, if male rat pups are castrated at or prior to birth, they fail to show male-typical sexual behavior as adult, even if they are given testosterone. But if the castration is not performed until a few days after birth, as adults, testosterone induces male-typical behavior.

In the above cases, three conclusion can be drawn.

It is too often that we view this kind of body development as a nature event, and we take it for granted. In fact, a newly fertilized egg already knows its adult body shape, what it shall be when it becomes an adult. It is not because that egg is a prophet, nor because there is a strict genetic determinism. It simply follows the past-future interaction (genes hierarchy and environmental forces).

It is the fact that today does interact with the future. The one child policy in China will determine (or alter) the demographic picture of Chinese society for decades to come. The budget debate in Capital Hill will determine the future fate of American society. The past also interacts with today and tomorrow. The words of Confucius are still directing the thinking process of every Chinese people.

But, physics today cannot explain where tomorrow is. Where is Yesterday? How does tomorrow become today? How do today and tomorrow interact? We do know that there is tomorrow and that tomorrow will always become today. The above examples (the development of life and society) clearly show that today does interact with the future.

Without being able to answer these questions, not only is the current mainstream physics not complete, but we will never truly be able to understand what life is. In my paper --- The Final TOE (Theory of Everything), presented at 19th World Congress of Philosophy in Moscow 1993, I did provide a model on where tomorrow is.

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V: Mutual Immanence

--- the metaphysical foundation of life and the linkage to physics, mathematics and theology

During mitosis (the replication of chromosomes), many billions of genetic codes have to be reproduced. With today's technology and quality control standard, a process produces only 200 defective products per million is considered to be a super reliable process. But, if there is only one error per billion during any chromosome reproduction, every species will lose its vital genetic traits in 10 generations. In the case of fruitfly, its compound eye requires that six photoreceptor cells (which look at one point in space) are connected to the same pair of neurons. A study traced 650 neurons, and none is connected to the wrong cells.

On the one hand, although the development of the human brain indeed appears to be programmed genetically, there has been much latitude and plays introduced in the execution of this program. Even the identical twin who are absolutely identical genetically will never have identical nervous systems. This amount of play is an expression of epigenesis. Thus, every human individual has inscribed in the very structure of the brain his or her own singular history.

Therefore, not only is there flexibility within genetic determinism, but there is an infinite possibility within the framework of absolute reliability. This absolute reliability guarantees that every human embryo (even with many defective genes) will in no doubt turn into a human. The infinite possibility guarantees that every individual is in no doubt a true individual.

Furthermore, the body development of any life has only one process --- the body development. But this singular process clearly constructs two absolute opposite trends.

Yet, these two opposite trends are accomplished by a single process. In fact, the only way to construct an organized structure from a singular beginning is to become chaotic (differentiate) first. That is, the chaos is the cause and the driving force for orderliness. In short, chaos and order are two sides of the same coin. By the same token, the absolute reliability and the infinite possibility are also two sides of the same coin.

This kind of relation between two absolute opposite trends, forces, or concepts is called mutual immanence. This concept of mutual immanence was invented (or discovered) by Chinese 5,000 years ago in terms of Yin and Yang. In time of conflict, Yin and Yang are opposite forces. In constancy, they not only complement each other but are imbedded in each other. After reaching their full strength, they transform into the opposites. That is, Yang becomes Yin and Yin becomes Yang. Thus, Yin (the weak one) can conquer Yang (the strong and powerful one) by yielding and allowing Yang to reach its full strength, then leads the ultimate conversion of Yang to Yin at end. This concept is not only a very powerful politic strategy but is the only way to understand the Final Truth.

The foundation of modern physics is the Principle of Complementarity which is expressed as Copenhagen Interpretation (CI) of Heisenberg Uncertainty Principle, and it consists of three parts.

  1. A whole (totality) must consist of two opposite parts.
  2. These two opposite parts must be mutually exclusive.
  3. These two opposite parts are complementary to each other.
The Copenhagen Interpretation is clearly not reflecting the true meaning of the Uncertainty Principle. When we want to get a more accurate position measurement of a particle (smaller delta x), we must pay for it with the price of knowing less accurate information on its momentum (larger delta p). That is, delta p transforms into delta x, just the same as the Yin-Yang transformation. Delta p and delta x are mutual inclusive (mutual immanence), not mutual exclusive. The Heisenberg uncertainty principle is, in fact, the principle of mutual immanence of physics.

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VI: Laws of body shape and brain structure

In fruitfly experiments, when one pair of legs can enlarge while the other pairs remain unchanged, the different segments must be under independent genetic control. When a pair of legs can fatten but not lengthen, the different leg axes can be controlled independently. Seemingly, genes are the best candidates for controlling the body shape. But, when humans and chimpanzees are compared, their proteins are found to be more than 99% identical in amino acid sequence. Many of the differences have no functional consequence, and thus it is hard to credit that they could be responsible for the morphological differences between the two species. Furthermore, some groups of species are very conservative and change little anatomically over long geological periods, others evolve at high rates. Yet when rates of change of protein sequences are compared in slow and fast evolving groups they are found to be about the same. Two species of fruitfly (D. Heteroneura and D. Sylvestries) with significant different head shapes can interbreed. D. W. Thompson observed that the body shape of one species could be transformed into that of another by simple proportionate changes in the different axes. He wrote, "There is something... indispensable ... In these transformations... every point that every line... keeps its relative order and position throughout all distortions... ."

Therefore, although body shape responds very rapidly to nature selection, the evolution still must follow the laws of geometry. In short, geometry is the controlling manager of body shapes, and genes are only blue collar workers.

In the human brain, it has 10 billion nerve cells (neurons) and 10 trillion connections (synapses) between the neurons. During the brain development, neurons undergo intense migratory activity. During its migration, each neuron projects out about 1,000 dendrites (short connections) and many axons (long connections) to make contact with other neurons to form neuronal networks. How does each neuron know where to go? How do the projections (dendrites and axons) find their way through the three-dimensional space of the brain matter? How do they recognize the cells (from billions of them) with which they must establish contact?

There is no way for each individual neuron to possess those super knowledge and answers on the above questions. The brain development is simply a neurons stampede. Those neurons did not make the correct connections must die. During embryogenesis of the brain, from 10 to 80% (depending on the regions) of the neurons die.

This phenomenon points out one very important conclusion. The human brain has a network structure which preexists the neurons stampede. Those migrating neurons must fit into that pre-designed structure or face the death. This pre-designed brain network must be topological in nature, so does the laws of body shape.

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VII: Symmetry and symmetry breaking

Most of insects or animals have left-right symmetry but not top-down or front-back. Perhaps, the top-down asymmetry could be caused by gravity, but how about the front-back asymmetry? Most plants do have four direction symmetry because they are unable to move around. Being able to turn round and round quickly, animals give up the front back symmetry because of the biological economy. But the symmetry breaking has much deeper metaphysical reason than just the simple biological economy.

In moth, the development of scale (nerve cells), one epidermal cell divides asymmetrically, giving an internal smaller daughter that degenerates. The outer cell divides again slightly obliquely to give an external cell that makes the socket, and an internal cell that makes the scale. Again, this cells differentiation (symmetry breaking) comes from the division of one mother cell, and thus it cannot be caused by action of genes alone but is associated with or caused by topology (location and the available space).

VIII: Conclusion

Symmetry and symmetry breaking are central points in physics, mathematics and lives. The topological symmetry breaking gives rise to the entire universe (time, space, mass and lives). This is the foundation of the Super Unified Theory.

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