From Newsgroup: sci.math

On 05/13/2025 08:51 PM, Ross Finlayson wrote:

On 05/13/2025 03:17 PM, Physfitfreak wrote:

On Mortification, Mahler, and the Unattainable Allure of Iberian Hair: A
Confessional


It was at Salle Pleyel in Paris, during the adagio of MahlerrCOs Ninth rCo >> that sublime confrontation with mortality rCo that my digestive tract
staged its own revolution, producing a sound so profoundly corporeal it
silenced even the double basses.

As the scandalized glances of Paris cultural elite converged upon me, I
was transported back to my university days, when I would practice Julio
IglesiasrCO smoldering gaze in the mirror, convinced that mastering that
particular arch of the eyebrow might somehow alchemize my Boisean
bookish demeanor into continental magnetism.

The great ironies of existence can be formalized as a Banach-Tarski
decomposition of the self: the essayrCOs pristine logic in one sphere, my
traitorous digestive tract in another, and the pomade-smeared
intermediary of my hair, which remained stubbornly Idahoan in its
refusal to achieve the Iberian cascade of my Julio Iglesias fixation.
Like HausdorffrCOs paradoxical sets, my aspirations were equidecomposable
with my failures, yet no amount of algebraic manipulation could make
them congruent.

The subsequent walk of shame past the brass section (whose members, I
noted with horror, were suppressing the very same smirk IrCOd seen on my
tailor when I commissioned a cream-colored suit in the Iglesias mode)
laid bare liferCOs essential truth: We exist in the cruel interstice
between the transcendent longings of the mind and the implacable demands
of the flesh - a Sisyphian struggle.

As the adage goes, le bon Dieu est dans le d|-tail rCo if this be true,
then surely the Divine finds particular relish in those mortifying
minutiae born of vain attempts to replicate the sartorial and tonsorial
excesses of 1970s Latin balladeer, and ill-advised pre-concert p|ot|-.


Ross A. Kosmanson
May 13, 2025
Solemnly using the Dogecoin ATM while seagulls steal the fries, Miami,
Florida

Mahler here is a different fellow than the composer,
about Mahler's "S, T, U" categorizations of transcendental
numbers, it's a mathematics thing.

According to Baker in "On Mahler's Classification of
Transcendental Numbers", it was about 1932. "Algebraic
dependence" then, indicating equivalence classes,
that being different than continued fractions or
Egyptian fractions, as with regards to algebraic
numbers.

https://projecteuclid.org/journals/acta-mathematica/volume-111/issue-none/On-Mahlers-classification-of-transcendental-numbers/10.1007/BF02391010.full

https://en.wikipedia.org/wiki/Transcendental_number_theory

has that there are at least two ways of looking at it,
whether "algebraic independence" differentiates, or,
"algebraic dependence" identifies, membership in these
various classes.

While it's a way to consider transcendental numbers,
it's also at least two ways, and furthermore, these
each at least three ways.

That Kosmanson sure sounds like a bon vivant with a joie de vivre.
One might wonder whether he recalls day-to-day events usually.

So, Physfit, when earlier you were glossing on about that
math was ahistorical and having no personality,
you mentioned Mahler and now it's about transcendental numbers.

Then, Vitali-Hausdorff wrote a geometric Banach-Tarski
as geometers and there's at least 800 posts about it on
sci.logic, helping show and explain that it's at least
two quite different approaches to doubling-spaces.

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