Look at all you phonies out there.
You poseurs.
All of you sheep. Counting 'til infinity. Counting sheep.
*pff*
What if I told you there were more there? Like, ... more than you can count?
But what would a sheeple like you know about more than infinity that you can count?
heh. *pff*
So, like, what does it mean to count til infinity? What does it mean to count more? And, like, where do dimensions fall in all of this?

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(Correction: at 12:00, the paradox is actually due to Galileo Galilei)
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56: More Sheep than You Can Count (Transfinite Cardinal Numbers)

Hosted by Gabriel Hesch and Autumn Phaneuf, who have advanced degrees in EE and industrial engineering/operations research respectively, come together to discuss mathematics as a pure field al in its own as well as how it describes the language of science, engineering, and even creativity. &nbsp;

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Technology

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Science

Mathematics

Physics

An interview with Prof. Marcus du Sautoy about his book Around the Wold in Eighty Games . . . .a Mathematician Unlocks the Secrets of the World's Greatest Games.  

Topics covered in Today's Episode: 

1. Introduction to Professor Marcus du Sautoy and the Role of Games

- Impact of games on culture, strategy, and learning

- The educational importance of games throughout history

2. Differences in gaming cultures across regions like India and China

3. Creative Aspects of Mathematics

4. The surprising historical elements and banned games by Buddha

5. Historical and geographical narratives of games rather than rules

6. Game Theory and Education

7.  Unknowable questions like thermodynamics and universe's infinity

8. Professor du Sautoy's Former Books and Collections

9.  A preview of his previous books and their themes

10. Gaming Cultures and NFTs in Blockchain

11. Gamification in Education

12. The Role of AI in Gaming

13. Testing machine learning in mastering games like Go

14. Alphago's surprising move and its impact on Go strategies

15 . The future of AI in developing video game characters, plots, and environments

16. Conclusion and Giveaway Announcement

*Free Book Giveaway of Around The World in 88 Games . . .  by Professor Marcus Du Sautory!  Follow us on our socials for details:  

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92. The Mathematical Heart of Games Explored with Prof. du Sautoy

Summary

Brain Organelles, A.I. and Defining Intelligence in  Nature- 

In this episode, we continue our fascinating interview with GT, a science content creator on TikTok [https://www.tiktok.com/@bearbaitofficial] and YouTube [https://www.youtube.com/@bearbaitofficial] known for their captivating - and sometimes disturbing science content.

GT can be found on the handle '@bearBaitOfficial' on most social media channels.  

In this episode, we resume our discussion on Brain Organelles -  which are grown from human stem cells - how they are being used to learn about disease, how they may be integrated in A.I.  as well as eithical concerns with them.

We also ponder what constitutes intelligence in nature, and even touch on the potential risks of AI behaving nefariously.

You won't want to miss this thought-provoking and engaging discussion.

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91.  Brain Organelles, AI, and Other Scary Science - An Interview with GT (Part 2)

This episode is inspired by a correspondence the Breaking Math Podcast had with the editors of Digital Discovery, a journal by the Royal Society of Chemistry.  In this episode the hosts review a paper [https://pubs.rsc.org/en/content/articlelanding/2024/dd/d3dd00077j] about how the Lean Interactive Theorem Prover, which is usually used as a tool in creating mathemtics proofs, can be used to create rigorous and robust models in physics and chemistry.  

Also -  we have a brand new member of the Breaking Math Team!  This episode is the debut episode for Autumn, CEO of Cosmo Labs, occasional co-host / host of the Breaking Math Podcast, and overall contributor who has been working behind the scenes on the podcast on branding and content for the last several months. Welcome Autumn!  

Autumn and Gabe discuss how the paper explores the use of interactive theorem provers to ensure the accuracy of scientific theories and make them machine-readable. The episode discusses the limitations and potential of interactive theorem provers and highlights the themes of precision and formal verification in scientific knowledge.  This episode also provide resources (listed below) for listeners interested in learning more about working with the LEAN interactive theorem prover.  

Takeaways

 * Interactive theorem provers can revolutionize the way scientific theories are formulated and verified, ensuring mathematical certainty and minimizing errors.
 * Interactive theorem provers require a high level of mathematical knowledge and may not be accessible to all scientists and engineers.
 * Formal verification using interactive theorem provers can eliminate human error and hidden assumptions, leading to more confident and reliable scientific findings.
 * Interactive theorem provers promote clear communication and collaboration across disciplines by forcing explicit definitions and minimizing ambiguities in scientific language. Lean Theorem Provers enable scientists to construct modular and reusable proofs, accelerating the pace of knowledge acquisition.
 * Formal verification presents challenges in terms of transforming informal proofs into a formal language and bridging the reality gap.
 * Integration of theorem provers and machine learning has the potential to enhance creativity, verification, and usefulness of machine learning models.
 * The limitations and variables in formal verification require rigorous validation against experimental data to ensure real-world accuracy.
 * Lean Theorem Provers have the potential to provide unwavering trust, accelerate innovation, and increase accessibility in scientific research.
 * AI as a scientific partner can automate the formalization of informal theories and suggest new conjectures, revolutionizing scientific exploration.
 * The impact of Lean Theorem Provers on humanity includes a shift in scientific validity, rapid scientific breakthroughs, and democratization of science. 

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90. LEAN Theorem Provers used to model Physics and Chemistry

This conversation explores the topic of brain organoids and their integration with robots. The discussion covers the development and capabilities of brain organoids, the ethical implications of their use, and the differences between sentience and consciousness. The conversation also delves into the efficiency of human neural networks compared to artificial neural networks, the presence of sleep in brain organoids, and the potential for genetic memories in these structures. The episode concludes with an invitation to part two of the interview and a mention of the podcast's Patreon offering a commercial-free version of the episode.



Takeaways

 * Brain organoids are capable of firing neural signals and forming structures similar to those in the human brain during development.
 * The ethical implications of using brain organoids in research and integrating them with robots raise important questions about sentience and consciousness.
 * Human neural networks are more efficient than artificial neural networks, but the reasons for this efficiency are still unknown.
 * Brain organoids exhibit sleep-like patterns and can undergo dendrite growth, potentially indicating learning capabilities.
 * Collaboration between scientists with different thinking skill sets is crucial for advancing research in brain organoids and related fields.

Chapters

 1.  00:00 Introduction: Brain Organoids and Robots
 2.  00:39 Brain Organoids and Development
 3.  01:21 Ethical Implications of Brain Organoids
 4.  03:14 Summary and Introduction to Guest
 5.  03:41 Sentience and Consciousness in Brain Organoids
 6.  04:10 Neuron Count and Pain Receptors in Brain Organoids
 7.  05:00 Unanswered Questions and Discomfort
 8.  05:25 Psychological Discomfort in Brain Organoids
 9.  06:21 Early Videos and Brain Organoid Learning
 10. 07:20 Efficiency of Human Neural Networks
 11. 08:12 Sleep in Brain Organoids
 12. 09:13 Delta Brainwaves and Brain Organoids
 13. 10:11 Creating Brain Organoids with Specific Components
 14. 11:10 Genetic Memories in Brain Organoids
 15. 12:07 Efficiency and Learning in Human Brains
 16. 13:00 Sequential Memory and Chimpanzees
 17. 14:18 Different Thinking Skill Sets and Collaboration
 18. 16:13 ADHD and Hyperfocusing
 19. 18:01 Ethical Considerations in Brain Research
 20. 19:23 Understanding Genetic Mutations
 21. 20:51 Brain Organoids in Rat Bodies
 22. 22:14 Dendrite Growth in Brain Organoids
 23. 23:11 Duration of Dendrite Growth
 24. 24:26 Genetic Memory Transfer in Brain Organoids
 25. 25:19 Social Media Presence of Brain Organoid Companies
 26. 26:15 Brain Organoids Controlling Robot Spiders
 27. 27:14 Conclusion and Invitation to Part 2

References:

Muotri Labs (Brain Organelle piloting Spider Robot) [https://pediatrics.ucsd.edu/research/faculty-labs/muotri-lab/index.html]

Cortical Labs (Brain Organelle's trained to play Pong) [https://corticallabs.com/]

*For a copy of the episode transcript, email us at breakingmathpodcast@gmail.com 

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Summary:

89.  Brain Organelles, AI, and the Other Scary Science - An Interview with GT (Part I)

This is a follow up on our previous episode on OpenAi's SORA [https://www.youtube.com/watch?v=LqQe3Fy9T9Y&t=611s]. We attempt to answer the question, "Can OpenAi's SORA model real-world physics?" 

We go over the details of the technical report, we discuss some controversial opinoins by experts in the field at Nvdia and Google's Deep Mind. 

The transcript for episode is avialable below upon request.


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56: More Sheep than You Can Count (Transfinite Cardinal Numbers)

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