Copyright

David H. Silver

Published On

2026-04-08

Language

  • English

Print Length

10 pages

THEMA

  • PH
  • PHQ
  • PHR
  • PDZ

BISAC

  • SCI055000
  • SCI015000
  • SCI057000
  • SCI061000
  • SCI075000
  • SCI034000

Keywords

  • Scientific storytelling
  • Conceptual physics
  • Modern physics explained
  • Relativity and quantum mechanics
  • Mathematics in science
  • Deep science for general readers

An Axiom of Your Choice

Chapter of: Beyond Popular Science

The Banach–Tarski paradox shows that a solid sphere can be partitioned into finitely many disjoint pieces and, using only rigid motions, reassembled into two spheres identical to the original. This construction depends on the Axiom of Choice and the existence of non-measurable sets, whose behavior diverges from intuitions about volume. While not physically realizable, the result reveals how certain set-theoretic assumptions allow decompositions that defy standard notions of size and conservation.

Contributors

David H. Silver

(author)
https://orcid.org/0000-0002-3071-304X

David H. Silver is an industrial researcher whose career bridges computer vision, computational biology, and science communication. He studied mathematics, computer science, and biology at the Technion — Israel Institute of Technology as a Rothschild Scholar, and was awarded a Microsoft Research PhD Fellowship for his doctoral work in computational biology at Cambridge, UK. Silver’s peer-reviewed publications span multiple domains: computational biology in Nature and PNAS; computer vision systems in IEEE Transactions on Pattern Analysis and Machine Intelligence; medical AI in Human Reproduction and MIDL; and entertainment analysis in PLoS One. He holds over a dozen patents in depth sensing, medical imaging, and generative AI. His industry positions include Algorithm Engineer at Intel Corporation, ML Researcher at Apple, and CTO/co-founder roles at several technology startups. Silver maintains academic collaborations with researchers worldwide and serves as a peer reviewer for Image and Vision Computing and PNAS.