The Rest Is Science Two Infinities (And Beyond)
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Mar 30, 2026 They trace ancient and medieval fear of the infinite and the theological and philosophical debates that followed. They revisit early paradoxes and surprising proofs that stretched mathematical thinking. They unpack Cantor’s diagonal argument and the discovery that some infinities are larger than others. They touch on how mathematical breakthroughs collided with personal and professional turmoil.
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Ancient Divide Between Process Infinity And Actual Infinity
- Ancient Greeks distinguished process infinities (like counting) from actual, physical infinities and accepted only the former.
- Aristotle and later thinkers treated physical infinity as impossible, prompting medieval debates about God's infinitude (Aquinas).
Harmonic Series Shows Summing Small Pieces Can Be Infinite
- Nicole Oresme showed harmonic series behavior where adding ever-smaller pieces can still diverge to infinity.
- This undermined Aristotle's idea that infinite results only arise from endless processes, proving summation can produce infinity.
Giordano Bruno Burned For Defending An Infinite Cosmos
- Giordano Bruno argued for an infinite universe and paid with imprisonment and execution by the Roman Inquisition.
- The Church saw physical infinity as a theological threat to doctrines like unique incarnation and salvation.