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Geometry and Sequence

yojiroyamanaka

The context matters. Without a context, nothing exists to be conceived.


What sets a context? The point of view of an observer. There is no single eternal uniform context - I think. The contexts form nested layers and are thus hierarchical. One context does not equal one point of view—no linear relationship. Multiple points of view can sometimes be permitted in one context. Different contexts usually provide other points of view. Two contexts in the same layer often have conflicts. To resolve the conflicts, they fight to surrender the other to prove the other was wrong. Unless people recognize the upper nested context that permits the presence of their context, two contexts in the same layer will fight for death until one eliminates the other.

 

My central question is whether an eternal uniform context (i.e., truth) exists. My answer is no. All contexts are part of nested contexts. Perhaps this is the limit of logic-based cognition, which inevitably creates infinite nestedness. A context sets a boundary. Only inside the boundary does the context-dependent logic work. We understand something by using logic, but outside is inconceivable. Cognizing outside with illogical imagination expands the understanding of our surrounding world and universe but inevitably sets a new boundary. Cognitive evolution occurs when a new idea breaks the boundary of the old context.

 

Does an eternal uniform law exist? Many in physics believe that. Some physicists are searching for eternal universal laws governing the material world, but we haven’t found them yet. Quantum probability suggests that the universe (our material world) is unlikely to be uniform, but with the force to be uniform—entropy. Our view of the universe has kept evolving with the trust of our ability to understand, which leads to improving our predictability of the future.


The only thing that has not changed during our evolving conception of the universe is our biological ability to understand - human perceptions (the ability of sense and cognition) since homo sapiens emerged on Earth. Nothing can be conceived without a context. Our brain might be the ultimate context of understanding.


Debates over the universe, geocentrism, heliocentrism, and Einstein's relativity are matters of context regarding where the centre is. In my view, all contexts are local or temporal. When we realize the outer context that permits the current context, the locality of the current context is also realized. Even if the current context looks uniform or eternally consistent, it must be a tentative illusion of human cognition.


Competition and selection are context-dependent. Without a context, there is no competition or selection. Replication is also context-dependent. Replication is the process of replicating a context that is nested within the surrounding context. Life is a replicable context within the surrounding local environment – local context.


The original local context permits replication- replicating a small context composed of limited numbers of units extracted from the original infinite units of the whole. For this to happen, the original context should not be uniform. Phase transitions like gas-liquid-solid, self-assembling and self-organizing create local nonuniformity and unevenness. This is geometry – the order in 3D space. Some geometry is identically reproducible if there is a template - replication, but others are reproducible but not identical, even if the context is identical. Reproducibility is not equal to replicability. They are two different concepts.

Imagine the water circulation in the ecosystem: evaporation, cloud formation, rain forming creaks, rivers, lakes, and pouring into oceans. These events reproducibly occur, but they do not replicate the previous ones. The path of a river has reproducible patterns, but it does not replicate any of them unless with human intervention.


Replication is a duplication or multiplication of the context. For replication, a boundary that defines the context is essential. The boundary does not need to be permanent. A spatially and temporally limited boundary can define the inner context (i.e. Self) if replication happens. The boundary is insufficient for making the Self – i.e. an exclusion is not the Self. The Self is the consequence of replication. An accidental replication connects the component of the replication process as the Self. Without Self, replication cannot be accomplished.


Geometry represents local unevenness in the 3D space. Interestingly, geometry can create an order in the proximity of components composing the geometry.  The order is one dimension. Some of the orders can link to a sequence of events. Geometry can create orders of proximity in molecules.  The order of proximity can create a sequence of bumping events between molecules- reactions.


Self-assembly inevitably creates an order. Polymers are a great example. Polymers can be composed of single minimal units or multiple minimal units. Some polymers have an orientation, and others don’t. Many biological polymers are composed of multiple minimal units with an orientation. There are no (or minimal) constraints in the sequence of minimal units; however, the sequence of polymers, like DNA, RNA and proteins, directly impacts their functions. Chemically and physically equivalent polymers can have different functions or no function based on their sequences. 


What are functions? Functions emerge only in the process of replication, similar to the Self. When two molecules bump, there are two possibilities: react or not react. Functions are one category of reactions. If a reaction is a part of the replication process, the reaction is called a function. Something needs to be accomplished for replication – the continuity of life.

Replication sets a nested inner context within an original context that has never been uniform or eternal.  The original local context permits the replication of the spatiotemporally defined nested context by a boundary within it.


Spontaneous emergences of geometry and associated sequential events happen in uneven sedimental conditions, facilitating phase transitions, self-assembly, and self-organization. In biology, the geometry of subcellular structures governs the sequences of biochemical events. Self-assembly of amino acids creates random peptides that each have their own geometry.   The sequence of DNA governs the sequence of amino acids that govern the geometry of proteins. The geometry of proteins governs the properties of self-organization, which creates the sub-cellular geometry of protein distributions. The geometry creates an order in proximity. The proximity dictates the probability of bumping and the sequence of bumping.


Reciprocal interactions between the geometry of materials and the sequence of events.  Once the geometry is established, it is reasonably stable as an equilibration, similar to the landscape. The geometry provides the context. But this context cannot replicate itself. The context can grow but not be alive. Life emerged as an accidental replication of the context within the larger original context. Life is the replicable context created by the balance of reciprocal interactions between growth and replication.


Replication is primarily the duplication of the inner context within the original context. The inner context can be duplicated by inheritance of the geometry and the sequence of DNA, but not either alone. Although the geometry can show growth, and DNA can be replicated in PCR, neither the geometry nor the sequence alone recreates life. Interestingly, life can be paused if the geometry and DNA sequence are intact - cryopreservation. The sequence of biochemical reactions can be stopped entirely and restarted if the geometry is preserved.  

Recent progress in synthetic embryos using multiple stem cell types provides new insight into the living state of a multicellular organism. Stem cells are alive at the cellular level but not at the organismal level. They are maintained in their alive state in in vitro culture. When they are placed in the alive context- a host embryo at the equivalent stage, those cells are integrated into the host to participate in their intrinsic developmental processes.


Interestingly, the context at the organismal level could be recreated by reconstituting the geometry of multiple stem cell types. The context of the developmental processes – i.e. the sequence of molecular/cellular events that create living organisms is hidden in the geometry of cell populations.  Disassembling or reassembling the geometry is sufficient to pause or resume the subsequent developmental processes.  The geometry is primarily self-organized, not by forced instructions when they are permitted to interact with each other. 

 

The history of human understanding is the identification process of the surrounding contexts. Conceiving a new context is the process of creating a new logical, intellectual field from unconceivable surroundings, like drawing nested circles. Each one needs to be a closed circle, but none should be fully closed in reality because everything we can conceive is connected and nested.


Life was created by an accidental replication process in a chaotic environment. Without partial closure by replication, life would never have started. Replication created a context to be replicated within the chaotic context. No context is independent from the upper or lower nested contexts. Inevitably, the history of human understanding of the universe and human society is discovering a new context over and over, often nested upper or lower. Infinite nestedness.


Probability is an interesting concept for dealing with this infinite. Probability permits capturing the idea of the infinite without creating a nested layer. After all, individual life is an infinite probability orchestrated by geometry and sequence.

 

 

 

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