Galileo's Paradox of Infinity — Lectures on Infinity (Lecture 6)

Comments · 18

• CH

  @christophedevos3760 · 11 hours ago

  Very interesting and clearly explained again, addictive lectures!

  3

• SH

  @shaiknagapasha · 13 hours ago

  Thank you sir 🙏

  1

• کٲ

  @کٲشر-ذ1ع · 2 hours ago

  Interesting 😮

• SU

  @surprisedmike · 8 hours ago

  Infinity is a useful mathematical abstraction that arises through approximation. Reality is finite and discrete, even though our perception might suggest otherwise,  as in believeing that motion is continuous. Believing in the existence of infinite objects in the real world produces paradoxes like the ones you discuss and that is pretty good evidence that there is something wrong with that belief. Careful use of infinity in science is fine but it is dangerous when people believe it is real. I see that in my own field (statistical inference) where such a belief produces, you guessed it, paradoxes.

  2

• BO

  @bookert2373 · 1 hour ago

  In mathematics, points and lines are idealized intellectual concepts, not physical entities. If you define a hypothetical line to be a collection of hypothetical points, then you get the Cantor ‘size’ comparisons; if, instead you define a hypothetical line to be a ‘direction’ lying between two hypothetical points, say a and b, then you can compare ‘sizes’ by comparing the difference b-a to that of other such ‘lines’.  The paradoxes arise when you demand that both distinct definitions must apply at same time.

• DO

  @DoDone-l7c · 10 hours ago (edited)

  <a href="https://www.youtube.com/watch?v=qlhoFL0hrWs&amp;t=922">15:22</a> length and width, like infinite life doesn&apos;t just mean length of one life but width of all life.

• DO

  @DoDone-l7c · 9 hours ago (edited)

  <a href="https://www.youtube.com/watch?v=qlhoFL0hrWs&amp;t=1376">22:56</a> maybe that infinite means open to change through relationships. Continuously because that&apos;s what infinity means, not just length but longevity, it&apos;s the Energizer bunny.

• DO

  @DoDone-l7c · 9 hours ago

  <a href="https://www.youtube.com/watch?v=qlhoFL0hrWs&amp;t=1507">25:07</a> each part is in relationship with all or infinity. The parts and whole are one.

• ER

  @ergo_org · 4 months ago (edited)

  📚 Watch the full series: <a href="https://www.youtube.com/playlist?list=PL1GBzfniaE7xWed_5aVa1wb4OR3aouNPx">https://www.youtube.com/playlist?list=PL1GBzfniaE7xWed_5aVa1wb4OR3aouNPx</a><br>▶️ Next: What Does Finite Really Mean? — Lectures on Infinity (Lecture 7) — <a href="https://www.youtube.com/watch?v=c_2GaOzx-bc">https://youtube.com/watch?v=c_2GaOzx-bc</a><br>🔗 Chapters, annotations &amp; multi-language subtitles: <a href="https://ergo.org/videos/joel-david-hamkins-galileos-paradox-of-infinity">https://ergo.org/videos/joel-david-hamkins-galileos-paradox-of-infinity</a><br><br>Presented by Ergo — free philosophy lectures at <a href="http://ergo.org/">ergo.org</a>

  1

• DO

  @DoDone-l7c · 9 hours ago (edited)

  <a href="https://www.youtube.com/watch?v=qlhoFL0hrWs&amp;t=1604">26:44</a> maybe all this is because the universe is emergent. Like the parts allow something to be born up through so it&apos;s got the whole with the part. Maybe it&apos;s equinumerous because it&apos;s emergent.

• DO

  @DoDone-l7c · 10 hours ago (edited)

  <a href="https://www.youtube.com/watch?v=qlhoFL0hrWs&amp;t=734">12:14</a> sounds like it shares something with Fibonacci.<br><a href="https://www.youtube.com/watch?v=qlhoFL0hrWs&amp;t=846">14:06</a> I have ideas I can&apos;t put into words dealing with your diagram, the Fibonacci sequence, euclidean geometry, and infinity. The increase in sides and points of contact lead me to seeing each point as infinitely small but also open sorta like water molecules building the ocean but also free in the ocean through the relationships.

• CH

  @christophedevos3760 · 11 hours ago (edited)

  Could the fault in Euclid also be related to his other fault with the parallel postulate? I don&apos;t know exactly what I&apos;m saying here but what seems to be true in a plane doesn&apos;t seem to hold on a sphere for instance?