Summary
Overview
This Field Notes episode explores mathematical concepts around zero, topology, and holes through listener questions. Michael and Hannah discuss why mathematics 'breaks' at certain scales, the importance of symmetry in human evolution, and the fascinating topology of everyday objects - from straws to the human body. The conversation culminates in an evolutionary history of the digestive system, explaining why humans are essentially seven-holed donuts.
The Problem with Zero in Mathematics
The hosts tackle a listener question about why scientists complain that math 'breaks' when encountering zeros. They explore the historical reluctance to adopt zero as a concept in Europe and discuss how mathematical equations fail at extreme scales - from fluid dynamics to black holes. Rather than mathematics being fundamentally broken, they argue that our equations simply reach the limits of their applicable scales, whether at the quantum level or near singularities.
- Zero wasn't commonly used in Britain until around Shakespeare's time, despite being used in India for much longer
- Mathematical singularities occur when denominators approach zero, causing equations to 'blow up' and lose correspondence with reality
- Equations work well at certain scales but fail when pushed to extremes - Newton's gravity works for humans throwing balls but not at cosmic or quantum scales
- Division by zero isn't actually division - it's like asking 'what's two plus tuna fish?' - one element isn't even a number
" Reality certainly isn't going, oh my gosh, there's a zero in the equation that we're all following. Time to what? Create a rip in space time? No, the fluid keeps flowing. "
" We're just modeling reality really well with math, but there's some fundamental like small scale in the universe where the universe does something different. "
Scientific Assumptions That Could Be Wrong
Hannah discusses fundamental assumptions in science that could potentially be disproven, with devastating consequences. She highlights dark matter as a theory that forms the basis of many careers but has never been directly observed, and introduces the rival theory of modified Newtonian dynamics (MOND) which suggests Einstein's equations might not work at galactic scales. She also questions whether physical constants have remained constant throughout cosmic history and critiques the reliability of the peer review system in scientific publishing.
- Dark matter was proposed to explain missing gravity in galaxies, but has never been directly found despite extensive research
- Modified Newtonian dynamics (MOND) suggests Einstein's equations might only work at solar system scales, not galactic ones
- Physical constants like Planck's constant may not have been constant throughout the universe's history or across all regions
- The peer review system has cracks - retractions are increasing and AI is making it easier to produce papers that sound legitimate
" There are people who spend their entire careers studying, analysing, trying to decipher what dark matter is. No one's ever found it. But I mean, there is quite good evidence that something like that exists. But there is this rival theory that says, well, what if Einstein was just wrong? "
" You're handing these papers that you're writing and you're handing them to volunteer scientists who've got their own stuff going on who maybe don't have time or the expertise to go through and check every single number and like quite a lot of stuff slips through "
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