Breaking Math PodcastMathematics

Breaking Math Podcast


Breaking Math Podcast

90. LEAN Theorem Provers used to model Physics and Chemistry

Sat, 16 Mar 2024

Help Support The Podcast by clicking on the links below:

Resources on the LEAN theorem prover and programming language can be found at the bottom of the show notes (scroll to the bottom). 

Summary

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 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 scienc

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

Tue, 05 Mar 2024


Help Support The Podcast by clicking on the links below:

Summary:
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)

Cortical Labs (Brain Organelle's trained to play Pong)

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



88. Can OpenAi's SORA learn and model real-world physics? (Part 1 of n)

Tue, 27 Feb 2024


Help Support The Podcast by clicking on the links below:

This is a follow up on our previous episode on OpenAi's SORA. 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.

87. OpenAi SORA, Physics-Informed ML, and a.i. Fraud- Oh My!

Tue, 20 Feb 2024

Help Support The Podcast by clicking on the links below:

Contact us at breakingmathpodcast@gmail.com

Summary

OpenAI's Sora, a text-to-video model, has the ability to generate realistic and imaginative scenes based on text prompts. This conversation explores the capabilities, limitations, and safety concerns of Sora. It showcases various examples of videos generated by Sora, including pirate ships battling in a cup of coffee, woolly mammoths in a snowy meadow, and golden retriever puppies playing in the snow. The conversation also discusses the technical details of Sora, such as its use of diffusion and transformer models. Additionally, it highlights the potential risks of AI fraud and impersonation. The episode concludes with a look at the future of physics-informed modeling and a call to action for listeners to engage with Breaking Math content.



Takeaways


  • OpenAI's Sora is a groundbreaking text-to-video model that can generate realistic and imaginative scenes based on text prompts.
  • Sora has the potential to revolutionize various industries, including entertainment, advertising, and education.
  • While Sora's capabilities are impressive, there are limitations and safety concerns, such as the potential for misuse and the need for robust verification methods.
  • The conversation highlights the importance of understanding the ethical implications of AI and the need for ongoing research and development in the field.


Chapters


00:00 Introduction to OpenAI's Sora

04:22 Overview of Sora's Capabilities

07:08 Exploring Prompts and Generated Videos

12:20 Technical Details of Sora

16:33 Limitations and Safety Concerns

23:10 Examples of Glitches in Generated Videos

26:04 Impressive Videos Generated by Sora

29:09 AI Fraud and Impersonation

35:41 Future of Physics-Informed Modeling

36:25 Conclusion and Call to Action


#OpenAiSora #

86. Math, Music, and Artificial Intelligence - Levi McClain Interview (Final Part)

Sun, 18 Feb 2024


Help Support The Podcast by clicking on the links below:

Transcripts are available upon request. Email us at BreakingMathPodcast@gmail.com

Follow us on X (Twitter)

Follow us on Social Media Pages (Linktree)


Visit our guest Levi McClain's Pages: 

youtube.com/@LeviMcClain

levimcclain.com/


Summary

Levi McClean discusses various topics related to music, sound, and artificial intelligence. He explores what makes a sound scary, the intersection of art and technology, sonifying data, microtonal tuning, and the impact of using 31 notes per octave. Levi also talks about creating instruments for microtonal music and using unconventional techniques to make music. The conversation concludes with a discussion on understanding consonance and dissonance and the challenges of programming artificial intelligence to perceive sound like humans do.



Takeaways:


  • The perception of scary sounds can be analyzed from different perspectives, including composition techniques, acoustic properties, neuroscience, and psychology.
  • Approaching art and music with a technical mind can lead to unique and innovative creations.
  • Sonifying data allows for the exploration of different ways to express information through sound.
  • Microtonal tuning expands the possibilities of harmony and offers new avenues for musical expression.
  • Creating instruments and using unconventional techniques can push the boundaries of traditional music-making.
  • Understanding consonance and dissonance is a complex topic that varies across cultures and musical traditions.
  • Programming artificial intelligence to understand consonance and dissonance requires a deeper understanding of human perception and cultural context.



Chapters

00:00 What Makes a Sound Scary

03:00 Approaching Art and Music with a Technical Mind

05:19 Sonifying Data and Turning it into Sound

08:39 Exploring Music with Microtonal Tuning

15:44 The Impact of Using 31 Notes per Octave

17:37 Why 31 Notes Instead of Any Other Arbitrary Number

19:53 Creating Instruments for Microtonal Music

21:25 Using Unconventional Techniques to Make Music

23:06 Closing Remarks and Questions

24:03 Understanding Consonance and Dissonance

25:25 Programming Artificial Intelligence to Understand Consonance and Dissonance

Send Message to Breaking Math Podcast

Unverified Podcast
Is this your Podcast? Claim It!

Podcaster File Breaking Math Podcast

Reviews for Breaking Math Podcast