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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: sci.logic
Subject: =?UTF-8?Q?Analogy_as_a_Core_of_Intelligence_=28Human_&_Artificial?=
 =?UTF-8?Q?=29_=28Was:_Gian-Carlo_Rota=e2=80=99s_legacy_and_modern_AI=29?=
Date: Thu, 17 Jul 2025 12:13:49 +0200
Message-ID: <105aics$2botd$1@solani.org>
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In-Reply-To: <105ahlr$2boci$2@solani.org>

Hi,

Rota often celebrated symbolic, analogical, and
conceptual understanding over brute calculation.
This philosophy has come full circle in modern AI:

- Large Language Models (LLMs) like GPT-4 don't
   just store facts — they recognize patterns,
   make analogies, and generate new structures
   from old ones.

- Rota’s work in combinatorics, symbolic logic, and
   operator theory is essentially pattern-based
   manipulation — exactly the kind of reasoning LLMs
   aim to emulate at scale.

Rota had a clear aesthetic. He valued clean formalisms,
symbolic beauty, and well-defined structures. Rota wanted
mathematics to mean something — to be not just correct,
but intelligible and expressive.

In contrast, modern AI (especially LLMs like GPT) thrives
on the messy, including: Noisy data , Inconsistency ,
Uncertainty, Contradiction. AI engineers today are mining
meaning from noise.

What counts as “structure” is often just the best
pragmatic/effective description available at that moment.

Bye

Mild Shock schrieb:
> Hi,
> 
> Spotting Trojan Horses is a nice example
> of creativity that also needs ground truth.
> Gian-Carlo Rota was phamous for this truth:
> 
> "The lack of understanding of the simplest
> facts of mathematics among philosophers
> is appalling."
> 
> You can extend it to GitHub acrobats,
> paper mill balerinas and internet trolls.
> But mathematics itself had a hard time,
> 
> allowing other objects than numbers:
> 
> - Blissard's symbolic method
>    He was primarily an applied mathematician and
>    school inspector. His symbolic method was a way
>    to represent and manipulate sequences algebraically
>    using formal symbols.
> 
> - Gian-Carlo Rota (in the 1970s)
>    Gian-Carlo Rota (in the 1970s) gave Blissard’s
>    symbolic method a rigorous algebraic foundation. Rota
>    admired the symbolic reasoning of 19th-century mathematicians
>    and often described it as having a “magical” or “mystical”
>    elegance — again hinting at interpretive, almost poetic, qualities.
> 
> - Umbral calculus
>    Modern formalization of this method, often involving
>    linear operators and algebraic structures. "Umbral"
>    means “shadow” — the power-like expressions are
>    symbolic shadows of actual algebra.
> 
> Bye
> 
> 
> Mild Shock schrieb:
>> Henri Poincaré believed that mathematical
>> and scientific creativity came from a deep,
>> unconscious intuition that could not be
>>
>> captured by mechanical reasoning or formal
>> systems. He famously wrote about how insights
>> came not from plodding logic but from sudden
>>
>> illuminations — leaps of creative synthesis.
>>
>> But now we have generative AI — models like GPT — that:
>>
>> - produce poetry, proofs, stories, and code,
>>
>> - combine ideas in novel ways,
>>
>> - and do so by processing patterns in massive
>>     datasets, without conscious understanding.
>>
>> And that does seem to contradict Poincaré's belief
>> that true invention cannot come from automation.
>