Journey to the edge of reason with Professor Hamkins!

Joel is a Professor of Philosophy and Mathematics at the University of Notre Dame. His research work spans Mathematical Logic and Set Theory.

You can find him here:

• Personal website: https://jdh.hamkins.org
• Twitter: https://twitter.com/JDHamkins
• Google Scholar: https://scholar.google.com/citations?user=MHLQDYQAAAAJ&hl=en&oi=ao

Back to the Stone Age is on:

• YouTube: https://youtube.com/playlist?list=PLZrhMJ5eusE_ACw6Ec3TqCbvDVZ6HP809&si=EHUZow_K4nlcWw8M
• Spotify: https://open.spotify.com/show/3pT8MUeR8bskcsuu8gmUGK?si=7f6f32052e9a4587
• Apple Podcasts: https://podcasts.apple.com/it/podcast/back-to-the-stone-age/id1741219288

Outline

00:00 - Introduction

00:55 - Mathematician or philosopher?

05:05 - Set Theory

09:52 - Is mathematics invented or discovered?

15:42 - Godel Incompleteness Theorem

24:14 - Infinity: potential and actual infinity

46:51 - Paradoxes on infinity

55:56 - Penrose three world model: mathematical, physical, and platonic world

01:00:21 - Mathematical reality

01:08:34 - Transfinite numbers, cardinals and ordinals

01:18:44 - The Absolute Infinity

01:25:08 - Infinity and time

01:30:57 - Irrational numbers, Alan Turing and computability

01:40:00 - Cantor’s definition of Set

01:43:40 - Cantor’s theorem

01:54:00 - Continuum Hypothesis

02:05:46 - Hostility of mathematician towards infinity

02:11:39 - Law of excluded middle and infinity

02:17:38 - Not finding answers to questions

02:19:58 - Is there more than maths permeating reality?

02:25:20 - AI and maths/physics

02:31:51 - AI and consciousness

02:36:36 - Most beautiful idea in mathematics and conclusion

Conversations with Friends: Greta Galluzzo.

Greta is a Psychology master's student and she's on Erasmus here in Amsterdam.

Find Back to the Stone Age on:

• YouTube: https://youtube.com/playlist?list=PLZrhMJ5eusE_ACw6Ec3TqCbvDVZ6HP809&si=WhVnrLLAUuYW-Any
• Spotify: https://open.spotify.com/show/3pT8MUeR8bskcsuu8gmUGK
• Apple Podcast: https://podcasts.apple.com/us/podcast/back-to-the-stone-age/id1741219288

Outline:

00:32 - Consciousness

06:32 - Animal consciousness and death

11:22 - Intelligence and language

17:18 - Empathy

20:01 - Awareness

22:35 - Mathematics

32:40 - Predisposition to mathematics, nature or nurture

35:20 - Acceptation of "limits" vs biological engineering to enhance human condition

44:15 - Is consciousness good or bad

47:06 - What is good and bad? Is there a universal ethics?

49:55 - Are humans good or bad?

52:12 - Happiness, suffering and altruism

01:10:47 - Being and feeling alive and dreaming state

01:23:19 - Greta's meaning of life

01:27:00 - Conclusion

Enjoy Back to the Stone Age!

Geetanjali is Associate Professor at St. Stephen’s College. She has a PhD in Cosmology from Delhi University. She's working on the Variable Chaplygin Gas model of dark energy.

Reach out to her on LinkedIn: https://www.linkedin.com/in/geetanjali-sethi-a7b201aa/?originalSubdomain=in

Find her research work on Google Scholar: https://scholar.google.com/citations?user=EK8KFB0AAAAJ

Back to the Stone Age is on:

- YouTube: https://youtube.com/playlist?list=PLZrhMJ5eusE_ACw6Ec3TqCbvDVZ6HP809&si=WhVnrLLAUuYW-Any

- Spotify: https://open.spotify.com/show/3pT8MUeR8bskcsuu8gmUGK

- Apple Podcast: https://podcasts.apple.com/us/podcast/back-to-the-stone-age/id1741219288

Outline

00:00 - Introduction

00:15 - Energy

02:53 - Dark matter and dark energy

10:15 - Dark energy as expansion of the universe

12:11 - Energy of empty space

17:08 - Heisenberg uncertainty principle

21:54 - Why dark energy has constant energy density

26:35 - Friedmann-Lemaitre-Robertson-Walker cosmological model

33:58 - Quintessence, modified gravity models

39:08 - Variable Chaplygin Gas model

39:40 - Cosmic fluid

43:34 - Differences with other models

48:19 - Fine-tuning in nature

53:31 - Combination of dark matter and dark energy

56:09 - Dependency of observations for the future of the universe

58:40 - Most interesting fact about the cosmos

59:24 - Making sense of enormous distances

01:05:42 - Will the universe expand forever?

01:11:38 - AI and science

01:13:01 - Limitations of human brain

01:17:45 - Conclusion