Part 12: Dialectical Arithmetics Series. Theorem: Arche'-Symbol's Exponent Equals Terms-Count of Resulting 'Cumulum'.

 

 

Theorem: Arche'-Symbol's Exponent Equals Terms-Count of Resulting 'Cumulum'.

 

Part 12: Dialectical Arithmetics Series.

 

 

 

 

 

Dear Reader,

 

 

 

It is my pleasure, and my honor, as an elected member of the Foundation Encyclopedia Dialectica [F.E.D.] General Council, and as a voting member of F.E.D., to share, with you, from time to time, as they are approved for public release by the F.E.D. General Council, key excerpts from the internal writings, and from the internal sayings, of our co-founder, Karl Seldon.

 

This 12th release of this new such series is posted below [Some E.D. standard edits have been applied, in the version presented below, by the editors of the F.E.D. Special Council for the Encyclopedia, to the direct transcript of our co-founder’s discourse]. 

 

 

 

 

Seldon –

 

 

 

 

 

 

 

 

For more information regarding these Seldonian insights, 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.

 

 

 

 

 

 

YOU are invited to post your comments on this blog-entry below!

 

 

 

 

 

 

 

 

 

 

 

Part 11: Dialectical Arithmetics Series. ‘Miguel’s Theorem’.

 

‘Miguel’s Theorem’.

 

Part 11: Dialectical Arithmetics Series.

 

 

 

 

 

Dear Reader,

 

 

 

It is my pleasure, and my honor, as an elected member of the Foundation Encyclopedia Dialectica [F.E.D.] General Council, and as a voting member of F.E.D., to share, with you, from time to time, as they are approved for public release by the F.E.D. General Council, key excerpts from the internal writings, and from the internal sayings, of our co-founder, Karl Seldon.

 

This 11th release of this new such series is posted below [Some E.D. standard edits have been applied, in the version presented below, by the editors of the F.E.D. Special Council for the Encyclopedia, to the direct transcript of our co-founder’s discourse].  

My thanks go to Dr. Seldon for honoring me by giving my name to this theorem.  Dr. Seldon is fond of saying, that he and the other, more senior, members of the Foundation should have seen the labor-saving technique guaranteed by this theorem first, but that they did not.  It was I who saw it first among us.

 

 

 

 

Seldon –

 

 

 

 

 

 

 

For more information regarding these Seldonian insights, 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.

 

 

 

 

 

 

YOU are invited to post your comments on this blog-entry below!

 

 

 

 

 

 

 

 

 

 

 

Part 01: Seldon’s Dialectics Series. ‘Dialectical Categorial/«Monad»-ic Combinatorics’.

 

‘Dialectical Categorial/«Monad»-ic Combinatorics’.

 

Part 01: Seldon’s Dialectics Series.

 

 

 

 

 

Dear Reader,

 

 

 

It is my pleasure, and my honor, as an elected member of the Foundation Encyclopedia Dialectica [F.E.D.] General Council, and as a voting member of F.E.D., to share, with you, from time to time, as they are approved for public release by the F.E.D. General Council, key excerpts from the internal writings, and from the internal sayings, of our co-founder, Karl Seldon.

 

This 1st release of this new such series is posted below [Some E.D. standard edits have been applied, in the version presented below, by the editors of the F.E.D. Special Council for the Encyclopedia, to the direct transcript of our co-founder’s discourse].

 

 

 

 

Seldon –

 

“The thing to remember about ‘dialectical categorial combinatorics’, and about the undergirding ‘monadic combinatorics’ of the monads or units which the category-«arithmoi» represent, is that not all monadic combinations are viable.  Indeed, perhaps most are not.”

 

“The task of users of a subject-matter Domain’s _NQ dialectical [meta-]model [meta-]equation is to discern what singleton monadic combination species, or what multitude of that species’ own sub-species of ontologically-distinct monadic combinations, are actually viable and already extant, or are expected/predicted, by a given user, to be viable, and to become manifest, in the future of the given subject-matter Domain.”

 

 

 

 

 

 

 

For more information regarding these Seldonian insights, 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.

 

 

 

 

 

 

YOU are invited to post your comments on this blog-entry below!

 

 

 

 

 

 

 

 

 

 

  

The Dialectical Opposition Between Rectilinearity versus Curvilinearity in Geometries.

  

The Dialectical Opposition Between Rectilinearity versus Curvilinearity in Geometries.

 

 

 

 

 

 

Dear Reader,

 

 

This blog-entry is to share, with you, a recent new Encyclopedia Dialectica ‘dialectogram’, presenting the systematic dialectic of the mathematical – geometrical -- categories of ‘rectilinearities versus curvilinearities’, posted above.  Note the 2-scales, finitary 'qualo-fractality' of that 'dialectogram'.

 

Perhaps the most interesting, most valuable aspect of this dialectic, is not the ‘categorial antithesis’, R ~ C, or, q_R ~ q_C, just stated above, but its ‘categorial synthesis’, q_CR.

 

The sub¹-species of that q_CR [sub⁰-]species represent some of the most important developments in the ancient-to-modern history of mathematics.

 

These include the derivation of the so-called “transcendental irrational” number, p, as the ‘reconciliator’ of the rectilinear Diameter of an ideal, “perfect” circle, with the curvilinear Circumference of such a circle:  p = C/D.

 

These also include the “differentiation operation” of the “differential calculus”, e.g., the limit of the ratio of the function-value, f(t + Dt) of a function, f, as Dt goes to[ward] 0, to its “argument” ‘augmentor’, (Dt) –

 

lim_(t ® 0)(Df(t+Dt)/(Dt))    ®    df(t)/dt

 

-- the latter, df(t)/dt, the “differential coefficient’, as the ‘reconciliator’ of the f(t) curve with the line of slope df(t)/dt, the [rectilinear] ideal tangent line, intersecting the ideal curvilinear locus of f(t), as t varies widely, but, for a given, specific value of t, representing that tangent line at only a single, ideal “point” of the f(t) curve, with the coordinates (t, f(t)).  

 

 

 

 

 

 

 

For more information regarding these Seldonian insights, 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.

 

 

 

 

 

 

YOU are invited to post your comments on this blog-entry below!