‘Mathematical Space Dynamicity’: A Mathematical Space that Self-Expands by Arithmetical Operation inside It, not Just in Volume, but in Dimensionality as well, to Model Ontology Expansion [‘Auto-Onto-Dynamasis’].

 

 

 

 

 

 

 

 

 ‘Mathematical Space Dynamicity’:

 

A Mathematical Space that Self-Expands by Arithmetical Operation inside It,

not Just in Volume, but in Dimensionality as well, to Model Ontology Expansion [‘Auto-Onto-Dynamasis’].

 

Dear Reader,

 

The space denoted by _NQ, the mathematical, analytical-geometric space of our standard _N Q_  axiomatic system of arithmetic, for the modeling of dialectics, is not a statical space, of fixed, unchanging volume and dimensionality, no matter what are the axiomatically-permitted arithmetical operations that ensue inside it.

 

No: On the contrary, the _NQ space is a space without closure, a maximally open space, which expands in volume, yes, but also in its dimensionality, with every arithmetical operation it hosts.

 

The “Natural Number” power of its root generic ‘meta-number’, denoted by q₁, corresponds to and generates the 

dimensionality of the _NQ space.

 

When that power is 1, only the 1-dimensional unit line segment which is the analytical-geometrical representative of q₁ constitutes that space.

 

When that power becomes 2, _NQ turns into a 2-dimensional space, represented arithmetically by the incommensurable diagonal line q₁ + q₂.

 

When that power rises to 3, _NQ becomes the 3-dimensional space, represented arithmetically by the ‘cubal’ incommensurable diagonal q₁ + q₂ + q₃.

 

When that power rises to 4, _NQ becomes the 4-dimensional space, represented arithmetically by the ‘hypercubal’ diagonal line q₁ + q₂ + q₃ + q₄.

 

And so on.

 

Turns out, this is exactly the kind of space needed to, purely-qualitatively, purely-ontologically, purely-categorially, model dialectical categorial progressions, both historical and systematic.

 

 

 

 

 

 

 

For more information regarding these Seldonian insights, and to read and/or download, free of charge, PDFs and/or JPGs of Foundation books, other texts, and images, please see:

 

www.dialectics.info

 

 

 

 

 

 

 

 

 

 

 

For partially pictographical, ‘poster-ized’ visualizations of many of these Seldonian insights – specimens of ‘dialectical art’ – as well as dialectically-illustrated books published by the F.E.D. Press, see:

 

https://www.etsy.com/shop/DialecticsMATH

 

 

 

 

 

 

 

 

 

 

 

¡ENJOY!

 

 

 

 

 

 

 

 

 

 

 

Regards,

 

 

 

Miguel Detonacciones,

 

Voting Member, Foundation Encyclopedia Dialectica [F.E.D.];

Elected Member, F.E.D. General Council;

Participant, F.E.D. Special Council for Public Liaison;

Officer, F.E.D. Office of Public Liaison.

 

 

 

 

 

 

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