90. LEAN Theorem Provers used to model Physics and Chemistry

03/16/24 • 47 min

1 Listener

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 science.

Help Support The Podcast by clicking on the links below:

Try out ZenCastr w/ 30% DiscountUse my special link to save 30% off your first month of any Zencastr paid plan
Patreon
YouTube
Breaking Math WebsiteEmail us for copies of the transcript!

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.

Help Support The Podcast by clicking on the links below:

Try out ZenCastr w/ 30% DiscountUse my special link to save 30% off your first month of any Zencastr paid plan
Patreon
YouTube
Breaking Math WebsiteEmail us for copies of the transcript!

Previous Episode

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

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

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

Help Support The Podcast by clicking on the links below:

Start YOUR podcast on ZenCastr!
Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan
Visit our Patreon

Summary:

Next Episode

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

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 and YouTube 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.
30% Off ZenCastr Discount

Use My Special Link to save e 30% Off Your First Month of Any ZenCastr Paid Plan