From Newsgroup: sci.physics


Hi,

The French Enlightenment (roughly 1700rCo1789)
produced extraordinary advances in mathematics,
science, and philosophy, but its concept of geometry
was still deeply tied to Euclid, and that limited
what even brilliant thinkers could imagine.

What was Euclid really doing?
https://www.youtube.com/watch?v=M-MgQC6z3VU

Amazingling during the French Engligment the
Parallel Postuale was not yet recognized as
independent. Rather we find:

- Adrien-Marie Legendre (1752rCo1833)
Repeatedly revised arguments to derive
the parallel postulate

- Joseph-Louis Lagrange (1736rCo1813)
Gave a lecture trying to derive the parallel
axiom from properties of similar triangles

Bye

Mild Shock schrieb:

Hi,

I always admired the French Teaching of Logic.
This silly Philosophy Professor scolded me a couple
of times with this nonsense, playing dumb and deaf,

like a complete idiot:

Me: LEM is derivable from RAA, in minimal logic.
Prof: LEM is not even derivable from RAA in intuitionistic logic.
Me: You didnrCOt use RAA as an inference schema!
Prof: Our discussion is about logic and not about Prolog. I apologize.

https://swi-prolog.discourse.group/t/needing-help-with-call-with-depth-limit-3/7398/78

Still his prover demonstrates LEM from RAA:

?-prove((a | ~a)).
\begin{prooftree}
\AxiomC{\scriptsize{1}}
\noLine
\UnaryInfC{$ \lnot (A \lor \lnot A)$}
\RightLabel{\scriptsize{$ \lor\to E$}}
\UnaryInfC{$ \lnot \lnot A$}
\AxiomC{\scriptsize{1}}
\noLine
\UnaryInfC{$ \lnot (A \lor \lnot A)$}
\RightLabel{\scriptsize{$ \lor\to E$}}
\UnaryInfC{$ \lnot A$}
\RightLabel{\scriptsize{$ \to E $}}
\BinaryInfC{$\bot$}
\RightLabel{\scriptsize{$ IP $} 1}
\UnaryInfC{$A \lor \lnot A$}
\end{prooftree} https://g4-mic.vidal-rosset.net/wasm/tinker#prove((a%20%7C%20~a)).

Please note that RAA = IP, synonymous names.
Reductio Ad Absurdum and Indirect Proof.

LoL

Bye

Mild Shock schrieb:

Hi,

In the coming age of analog computing,
symbolic logic means nothing:

rCLThe high data-rate sense perception and
identification abilities of the human system
mostly bypass verbal/analytic awareness. We
are generally conscious of a cognitive
recognition after the fact. In this way, what
we understand as consciousness has to be
identified as a reflexive monitoring ability
with quite limited application. To produce
consciousness (artificial or otherwise) we
are stepping down, not up.rCY
rCo Frank Herbert, Destination: Void

Bye

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.physics

Hi,

Even Rene Descartes was not aware of the
independence. DescartesrCOs failure has the same
underlying cause as later ones.

His algebraic setup already assumes Euclidean
geometry. He used geometric intuitions that were
secretly equivalent to EuclidrCOs axiom. He

lacked the concept of alternate geometries.

What an AI could have done (According to ChatGPT):

(A) Reveal hidden assumptions in every failed proof
An AI could:
- symbolically analyze the proof
- extract all uses of implicit Euclidean intuition
- point out: rCLThis step assumes that similar triangles
can be scaled arbitrarily, which is equivalent to
the parallel postulate.rCY

That kind of meta-analysis was unavailable to human
mathematicians of the time.

(B) Construct explicit models of non-Euclidean geometries
The big conceptual leap of the 19th century was the ability
to imagine a consistent geometry in which the parallel
postulate is false.

An AI could directly produce:
- the Poincar|- disk model
- the hyperboloid model
- the upper half-plane model

and demonstrate that all of EuclidrCOs axioms (except the
parallel postulate) hold in these spaces.

(C) Clarify the logical structure of axioms
HilbertrCOs axiomatization (1899) came very late, but
an AI could produce a clean formal structure centuries earlier:
- incidence axioms
- order axioms
- congruence axioms
- continuity axioms

parallel axiom as a separate toggle
This framework itself would have been revolutionary.

Bye

Disclaimer: Not sure how much of (A), (B) and (C) are
fact or fuction. Don't have Google DeepMind company
badge. See my other post

Subject: Turing-Test to Birch++-Test [Professor Yang-Hui He]
Date: Wed, 10 Dec 2025 14:55:28 +0100

Mild Shock schrieb:

Hi,

The French Enlightenment (roughly 1700rCo1789)
produced extraordinary advances in mathematics,
science, and philosophy, but its concept of geometry
was still deeply tied to Euclid, and that limited
what even brilliant thinkers could imagine.

What was Euclid really doing?
https://www.youtube.com/watch?v=M-MgQC6z3VU

Amazingling during the French Engligment the
Parallel Postuale was not yet recognized as
independent. Rather we find:

- Adrien-Marie Legendre (1752rCo1833)
-a Repeatedly revised arguments to derive
-a the parallel postulate

- Joseph-Louis Lagrange (1736rCo1813)
-a Gave a lecture trying to derive the parallel
-a axiom from properties of similar triangles

Bye

Mild Shock schrieb:

Hi,

I always admired the French Teaching of Logic.
This silly Philosophy Professor scolded me a couple
of times with this nonsense, playing dumb and deaf,

like a complete idiot:

Me: LEM is derivable from RAA, in minimal logic.
Prof: LEM is not even derivable from RAA in intuitionistic logic.
Me: You didnrCOt use RAA as an inference schema!
Prof: Our discussion is about logic and not about Prolog. I apologize.

https://swi-prolog.discourse.group/t/needing-help-with-call-with-depth-limit-3/7398/78

Still his prover demonstrates LEM from RAA:

?-prove((a | ~a)).
\begin{prooftree}
\AxiomC{\scriptsize{1}}
\noLine
\UnaryInfC{$ \lnot (A \lor-a \lnot A)$}
\RightLabel{\scriptsize{$ \lor\to E$}}
\UnaryInfC{$ \lnot-a \lnot A$}
\AxiomC{\scriptsize{1}}
\noLine
\UnaryInfC{$ \lnot (A \lor-a \lnot A)$}
\RightLabel{\scriptsize{$ \lor\to E$}}
\UnaryInfC{$ \lnot A$}
\RightLabel{\scriptsize{$ \to E $}}
\BinaryInfC{$\bot$}
\RightLabel{\scriptsize{$ IP $}-a 1}
\UnaryInfC{$A \lor-a \lnot A$}
\end{prooftree} https://g4-mic.vidal-rosset.net/wasm/tinker#prove((a%20%7C%20~a)).

Please note that RAA = IP, synonymous names.
Reductio Ad Absurdum and Indirect Proof.

LoL

Bye

Mild Shock schrieb:

Hi,

In the coming age of analog computing,
symbolic logic means nothing:

rCLThe high data-rate sense perception and
identification abilities of the human system
mostly bypass verbal/analytic awareness. We
-a-a are generally conscious of a cognitive
recognition after the fact. In this way, what
we understand as consciousness has to be
identified as a reflexive monitoring ability
with quite limited application. To produce
consciousness (artificial or otherwise) we
are stepping down, not up.rCY
rCo Frank Herbert, Destination: Void

Bye

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.physics

On 12/10/2025 12:34 PM, Mild Shock wrote:

Hi,

Even Rene Descartes was not aware of the
independence. DescartesrCOs failure has the same
underlying cause as later ones.

His algebraic setup already assumes Euclidean
geometry. He used geometric intuitions that were
secretly equivalent to EuclidrCOs axiom. He

lacked the concept of alternate geometries.

What an AI could have done (According to ChatGPT):

(A) Reveal hidden assumptions in every failed proof
An AI could:
- symbolically analyze the proof
- extract all uses of implicit Euclidean intuition
- point out: rCLThis step assumes that similar triangles
can be scaled arbitrarily, which is equivalent to
the parallel postulate.rCY

That kind of meta-analysis was unavailable to human
mathematicians of the time.

(B) Construct explicit models of non-Euclidean geometries
The big conceptual leap of the 19th century was the ability
to imagine a consistent geometry in which the parallel
postulate is false.

An AI could directly produce:
- the Poincar|- disk model
- the hyperboloid model
- the upper half-plane model

and demonstrate that all of EuclidrCOs axioms (except the
parallel postulate) hold in these spaces.

(C) Clarify the logical structure of axioms
HilbertrCOs axiomatization (1899) came very late, but
an AI could produce a clean formal structure centuries earlier:
- incidence axioms
- order axioms
- congruence axioms
- continuity axioms

parallel axiom as a separate toggle
This framework itself would have been revolutionary.

Bye

Disclaimer: Not sure how much of (A), (B) and (C) are
fact or fuction. Don't have Google DeepMind company
badge. See my other post

Subject: Turing-Test to Birch++-Test [Professor Yang-Hui He]
Date: Wed, 10 Dec 2025 14:55:28 +0100

Mild Shock schrieb:

Hi,

The French Enlightenment (roughly 1700rCo1789)
produced extraordinary advances in mathematics,
science, and philosophy, but its concept of geometry
was still deeply tied to Euclid, and that limited
what even brilliant thinkers could imagine.

What was Euclid really doing?
https://www.youtube.com/watch?v=M-MgQC6z3VU

Amazingling during the French Engligment the
Parallel Postuale was not yet recognized as
independent. Rather we find:

- Adrien-Marie Legendre (1752rCo1833)
Repeatedly revised arguments to derive
the parallel postulate

- Joseph-Louis Lagrange (1736rCo1813)
Gave a lecture trying to derive the parallel
axiom from properties of similar triangles

Bye

Mild Shock schrieb:

Hi,

I always admired the French Teaching of Logic.
This silly Philosophy Professor scolded me a couple
of times with this nonsense, playing dumb and deaf,

like a complete idiot:

Me: LEM is derivable from RAA, in minimal logic.
Prof: LEM is not even derivable from RAA in intuitionistic logic.
Me: You didnrCOt use RAA as an inference schema!
Prof: Our discussion is about logic and not about Prolog. I apologize.

https://swi-prolog.discourse.group/t/needing-help-with-call-with-depth-limit-3/7398/78

Still his prover demonstrates LEM from RAA:

?-prove((a | ~a)).
\begin{prooftree}
\AxiomC{\scriptsize{1}}
\noLine
\UnaryInfC{$ \lnot (A \lor \lnot A)$}
\RightLabel{\scriptsize{$ \lor\to E$}}
\UnaryInfC{$ \lnot \lnot A$}
\AxiomC{\scriptsize{1}}
\noLine
\UnaryInfC{$ \lnot (A \lor \lnot A)$}
\RightLabel{\scriptsize{$ \lor\to E$}}
\UnaryInfC{$ \lnot A$}
\RightLabel{\scriptsize{$ \to E $}}
\BinaryInfC{$\bot$}
\RightLabel{\scriptsize{$ IP $} 1}
\UnaryInfC{$A \lor \lnot A$}
\end{prooftree}
https://g4-mic.vidal-rosset.net/wasm/tinker#prove((a%20%7C%20~a)).

Please note that RAA = IP, synonymous names.
Reductio Ad Absurdum and Indirect Proof.

LoL

Bye

Mild Shock schrieb:

Hi,

In the coming age of analog computing,
symbolic logic means nothing:

rCLThe high data-rate sense perception and
identification abilities of the human system
mostly bypass verbal/analytic awareness. We
are generally conscious of a cognitive
recognition after the fact. In this way, what
we understand as consciousness has to be
identified as a reflexive monitoring ability
with quite limited application. To produce
consciousness (artificial or otherwise) we
are stepping down, not up.rCY
rCo Frank Herbert, Destination: Void

Bye

What if the other independent postulate
to "parallel lines meet at infinity"
is "lines have two angles at zero".

Of course, axiomless natural deduction
for axiomless geometry then making for
that Euclid's geometry a model thereof
naturally arises from reason itself,
makes for that axiomless geometry that
makes Euclidean geometry as an example,
is a thing.


DesCartes had plenty going on with regards
to vortices and their spirals and mechanics,
Poincare after Dirichlet gets a usual idea
that much like Euclid's "smooth" plane is
Poincare's "rough" plane.


When "AI Math" met DesCartes, ....


DesCartes was more than an Occam's nominalist,
about enlightenment/renaissance and rationality/idealism.

Deconstructive accounts may be variously structuralist.


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