LECTURE PAR L’AUTEUR
Écouter le poème.
Lu par A.F. King dans la version anglaise originale.
Banach–TarskiA.F. King · Lecture en anglais
POÈME + PARADOXE
Banach–Tarski
Humpty Dumpty découvre, quelques siècles trop tard, que la théorie des ensembles a rendu le réassemblage plus étonnant encore que la réparation.
CONCEPTUAL VISUALIZATION
One sphere, two spheres.
This deliberately simplified animation communicates the conceptual shock of the paradox. It is not the actual decomposition and should not be presented as a proof.
Conceptual only: the genuine theorem uses non-measurable sets, not five ordinary wedges that could be cut with a knife.
THE MATHEMATICIANS
Banach and Tarski.
EMPLACEMENT DU MÉDIAStefan Banach
/media/banach-tarski/stefan-banach.jpgStefan Banach
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EMPLACEMENT DU MÉDIAAlfred Tarski
/media/banach-tarski/alfred-tarski.jpgAlfred Tarski
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NURSERY RHYME MEETS SET THEORY
The king’s men were working in the wrong century.
EMPLACEMENT DU MÉDIAHumpty Dumpty
/media/banach-tarski/humpty-dumpty.jpgHumpty Dumpty
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Add a compact treatment of how the nursery rhyme supplies the poem’s body, fall, failed reconstruction, and comic outrage at discovering that abstract mathematics permits something far stranger than repair.
THE ACTUAL MATHEMATICS
Why does such a decomposition exist?
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LOCAL PROOF · PDF
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External source
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DISCUSSION DES LECTEURS
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